WASHINGTON — Secretary of State Hillary Rodham Clinton said Sunday that the United States will maintain a strong military interest in Iraq after the last combat troops leave this year, and she warned Iran not to try and take advantage of the pullout.

On television talk shows Sunday morning, Clinton said that no one, especially Iran, should underestimate America’s commitment to preserve the hard-fought gains of the past eight years.

“We have a lot of presence in that region,” Clinton said on CNN. “No one, most particularly Iran, should miscalculate about our commitment … to the Iraqis.”

After a week during which Moammar Gadhafi was killed, the U.S. also vowed partnership with the Libyan people as they build a new society – one that U.S. officials insist should begin with investigations Gadhafi death and with the imprisonment of the convicted Lockerbie bomber who is living free in Libya.

With Libya’s Transitional National Council putting together a new government, Clinton conveyed those requests while visiting Libya and elsewhere in the region last week.

As the U.S. reduces its presence in one country and turns its attention to reconstruction of another, the Obama administration is trying to promote security and the rule of law over strong local and regional interests.

Republicans question whether the departure of the remaining 40,000 American troops from Iraq by year-end serves those ideals, especially given recent threats by the Iranian president to get involved in the training of Iraqi troops.

Though the U.S. departure announced by President Barack Obama is in keeping with a schedule set by the George W. Bush administration, Republican critics say the president is opening the door to Iranian involvement.

The withdrawal is a “serious mistake,” Sen. John McCain said in on ABC’s “This Week,” and is “viewed in the region as a victory for the Iranians.”

“Once the military is gone, embassy personnel will be targets,” McCain said. “The fact that we have other bases in the region would have very little impact on Iraq itself.”

But Clinton strongly suggested that the U.S. will maintain a military presence in the region, and a willingness to respond to any Iranian threat.

“Iran should look at the region,” Clinton said on NBC. “We may not be leaving military bases in Iraq, but we have bases elsewhere. We have support and training assets elsewhere. We have a NATO ally in Turkey. … I don’t think anyone should be mistaken about America’s commitment to the new democracy in Iraq that we have sacrificed so much to help them achieve.”

News reports and images from the region show that Gadhafi leader was beaten and taunted by a crowd in his hometown of Sirte before his death, raising questions about the government’s assertion that he was killed in crossfire.

Administration officials voiced concern about what the reports portend for the rule of law and the establishment of civil institutions in Libya. U.S. diplomats said over the weekend that they support the United Nations’ call for an independent investigation of Gadhafi’s death.

On Sunday, Clinton made that position public and expressed support for the investigation the transitional council says it will conduct. Clinton also said she told Libyan officials that the U.S. wants Abdelbaset al-Megrahi, the convicted Lockerbie bomber, to serve the rest of his life sentence. Megrahi was released from a Scottish prison two years ago on humanitarian grounds because he had from cancer and was said to have three months left to live.

Although the United States wants Megrahi returned to Scotland, Clinton said Sunday only that Scotland was the “preferable” place for him to serve his sentence.

The new government in Libya must “start with the rule of law,” Clinton said, with “accountability, unity and reconciliation.”

Gadhafi loyalists should be safe in Libya and be included in the new government, she said, “as long as they don’t have blood on their hands.”

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