LOUSSVILLE, Ky.  — Sen. Rand Paul of Kentucky entered the campaign for the 2016 Republican presidential nomination Tuesday with a declaration that he’s running for the White House to “return our country to the principles of liberty and limited government.”

That message posted on his website prefaced a kickoff speech later in the day in Louisville.

“I am running for president,” his web message said. In remarks to supporters, Paul could be counted on to be a fierce critic of Washington, where he is in his first term as a senator but seldom in line with his party’s leadership.

Paul’s challenge now is to convince Republican primary voters and caucus-goers that his is a vision worthy of the GOP presidential nomination, a prize twice denied his father, former Rep. Ron Paul of Texas.

Paul begins the 2016 race as just the second fully declared candidate, behind Sen. Ted Cruz of Texas, but he could face as many as 20 rivals for the nomination before the lead-off Iowa caucuses in February.

Along the way, Paul is likely to challenge his fellow Republicans’ views on both foreign and domestic policy, as well as the nuts and bolts of how campaigns are run. Tech savvy and youth-focused, Paul is expected to be an Internet juggernaut that his competitors will be forced to chase.

After his speech in Louisville, Paul was set to answer questions from voters on his Facebook page. Before his announcement speech, he was already selling on his website iPhone cases branded with his logo, signed copies of the Constitution and Rand Paul beer steins.

The online store was a quick way for Paul to collect contact information for voters who want the swag but had not yet considered a direct donation to the candidate.

It’s unclear, though, how much support Paul can muster in the Republican mainstream.

Paul is a frequent contrarian against his party’s orthodoxy, questioning the size of the U.S. military and proposing relaxation of some drug laws that imprison offenders at a high cost to taxpayers. He also challenges the GOP’s support for surveillance programs, drone policies and sanctions on Iran and Cuba.

But as the presidential campaign came closer, Paul has shifted his approach somewhat on the complicated question about how much government the country actually needs.

“The issue on Sen. Paul and national security issues is where he comes down in the continuing conflict between his principles and his ambition,” said John Bolton, a former ambassador to the United Nations and a potential Paul rival for the GOP nomination.

In an interview, Bolton cited Paul’s shifting views on military spending.

In Paul’s proposal for the 2012 budget, he called for reducing military spending and for fewer troops at the Department of Defense. “The DOD should not be treated sacrosanct with regard to the treatment of taxpayer dollars,” Paul wrote in a plan that would balance the federal budget in five years.

But last month Paul proposed a 16 percent increase in the Pentagon’s budget.

“On any given day, it’s hard to know where he will be,” Bolton said. “I believe in redemption, and I hope he comes all the way over. But I just don’t know what’s at work in his mind.”

In another sign of his uphill climb, an outside group not connected to any candidate planned to spend more than $1 million on ads criticizing Paul’s positions on Iran sanctions. The ads were scheduled to start airing as Paul was declaring himself a candidate.

Perhaps reflecting the challenges he faces in convincing his critics he deserves the nomination, Paul is also leaving open the door to a second term in the Senate. With the backing of his state’s senior senator, Majority Leader Mitch McConnell, Paul is likely to seek the White House and the Senate seat at the same time.

McConnell was not expected to attend Paul’s political rally on Tuesday, instead opting for a meeting with the Jessamine County Chamber of Commerce near Lexington.

One of Paul’s likely rivals, Sen. Marco Rubio of Florida, has said he would not double-dip on the ballot. He is expected to announce next week that he will skip a Senate re-election bid in 2016 in favor of putting everything into a presidential campaign.

Where Rand Paul stands on the issues

By Adam Beam Associated Press

FRANKFORT, Ky. — A look at where Kentucky Sen. Rand Paul, who is set to declare his candidacy for the 2016 Republican presidential nomination Tuesday, stands on some issues:

IMMIGRATION

A thorny issue for Paul. He sees himself as a “different kind of Republican” and has encouraged his party to abandon its fixation on “amnesty,” saying the concept has trapped Republicans from embracing compromise. Yet Paul has spent considerable time trying to block or undo immigration proposals offered by others. In 2013 he voted against an immigration overhaul pushed by Republican Sens. John McCain and Lindsey Graham. He also introduced legislation that sought to undo President Barack Obama’s executive orders to delay deportation of some immigrants in the country illegally. He likes to say Washington “can’t invite the whole world” to the United States.

FOREIGN POLICY/NATIONAL SECURITY

Paul favors a smaller U.S. military presence overseas and opposes domestic surveillance programs, drawing from a libertarian ideology that has put him at odds with GOP donors and policymakers who see him as too soft for the world stage. He started to rein in those tendencies with the approach of his campaign. Paul cited the rise of violence in the Middle East to call for a declaration of war against the Islamic State group, arguing Congress alone has the constitutional power to declare war. And in March he proposed an increase in military spending. He drew support from some on the left as well as the right with a nearly 13-hour Senate speech centered on his opposition to U.S. policy on the use of military drones.

BUDGETS AND ENTITLEMENTS

The government is too big and needs to give money back to the taxpayer. That’s the essence of Paul’s position. He wants to lower the tax rate on overseas corporate profits that are returned to the U.S., and use such money for roads and bridges. He’d create “economic freedom zones” where individual and corporate income taxes are eliminated or drastically reduced in poor areas for 10 years.

EDUCATION

Kentucky was the first state in the country to adopt the Common Core standards for English and math in 2010, the year Paul was first elected to the Senate. It’s a good thing state leaders did not ask Paul about it, because the Kentucky senator has since come out strongly against the standards as they’ve become a flashpoint in national politics. Paul says the standards represent a chipping away of local control of education, despite the fact each state must vote to adopt them. He sees Common Core as a “hodgepodge of education theories” and “bureaucratic group think” that would collect massive amounts of data on school children for the government’s “social indoctrination.”

SOCIAL ISSUES

He opposes a federal ban on gay marriage, arguing states should decide for themselves, and says the Republican Party has room for people on both sides of the issue. Paul was criticized recently for a 2013 interview that resurfaced online in which he said he has never used the term “gay rights” because he doesn’t believe “in rights based on your behavior.” He also told pastors of a “moral crisis that allows people to think that there would be some other form of marriage.” He’s backed legislation that sought to ban abortion, yet upset some social conservatives by saying U.S. public opinion is too divided to change federal abortion laws. He’s urged GOP leaders to focus less on gay marriage and abortion as a way to help the party grow.

CLIMATE CHANGE

Kentucky is the nation’s third-largest coal producer, prompting most Kentucky politicians essentially to swear a loyalty oath to the coal industry. On one hand, Paul has denounced the government’s new emission regulations as part of President Barack Obama’s “war on coal.” On the other hand, Paul says he supports some coal regulations. During the debate on whether to authorize construction of the Keystone XL pipeline, Paul was one of 15 Republicans who voted for a measure that said humans contribute to the planet’s global warming problems.

CRIMINAL JUSTICE

This is an issue that largely sets Paul apart from the rest of the Republican field. He wants to restore voting rights to nonviolent convicted felons, eliminate mandatory minimum sentences, end the federal sentencing disparities between crack and powder cocaine and make it easier for people to expunge their criminal records. He has partnered with Democrats on most of those issues, which might broaden his appeal nationally should he win the GOP nomination.

Associated Press writer Philip Elliott contributed to this report from Washington.