WASHINGTON — Pentagon officials are weighing whether to cancel the last of three ships in General Dynamics Corp.’s $22 billion program to build new destroyers even though the vessel is already under construction at Bath Iron Works.

Canceling the USS Lyndon B. Johnson, a Zumwalt-class destroyer, is a topic that’s “to be reviewed in the next few weeks” by teams formed by the Pentagon’s independent cost- assessment office, according to a Defense Department briefing document dated Aug. 25. Two officials familiar with the issue confirmed that cancellation discussions are under way although no decision has been made.

The Zumwalt-class destroyer is designed as a multimission land-attack vessel that will use electricity generated by gas turbines to power all of its systems, including weapons. The cancellation discussions, part of planning for the fiscal 2017 budget, are the latest twist for a program that’s been buffeted by delays, rising costs and changing plans.

From an initial 32, the quantity planned was reduced over the years to seven and then three. The estimated procurement cost for all three vessels has increased by 37 percent since 2009 to $12.3 billion, according to the Congressional Research Service.

The estimated construction cost for the third destroyer, designated DDG-1002, is about $3.5 billion. A key question is how much of that could be saved by canceling a ship that’s about 41 percent complete, according to the officials, who asked not to be identified discussing internal deliberations.

A practical consideration for Defense Department officials is whether they can get away with canceling the ship considering the program’s strong support in Congress. Lawmakers rejected a Navy plan in 2008 to limit the Zumwalt class to two ships.

The ships are built at General Dynamics’ Bath Iron Works shipyard in Maine. Sen. Angus King of Maine, an independent, sits on the Senate Armed Services Committee, and the state’s other senator, Republican Susan Collins, heads a Senate Appropriations subcommittee and serves on its defense panel.

Asked about discussions of a potential cancellation, Commander Thurraya Kent, a Navy spokeswoman, said “it would be inappropriate to discuss business-sensitive information or speculate on budget deliberations.”

The ship was reviewed last month as part of a regularly scheduled meeting, and “the internal discussions of this meeting are not publicly releasable,” Kent said in an e-mail.

Lucy Ryan, a General Dynamics spokeswoman, said in an e- mail, “We’re not going to speculate” on any future Navy budget action. “This decision is entirely up to the Navy.”

The Navy is reviewing a Bath Iron Works proposal to adjust target costs for the second and third vessels in the class, with an updated proposal planned for December, according to a Navy program update last month.

Raytheon Co. makes the vessel’s combat and mission systems. The Navy is renegotiating with Raytheon to revise the contract options for mission systems for fiscal 2015 to 2017, according to the briefing document. Huntington Ingalls Industries Inc. builds the vessel’s composite deckhouse.

Separately, the Navy said delivery of the first vessel will slip beyond November, which was already 14 months later than originally scheduled. Kent said contractor-sponsored dockside tests would start in November, followed in December by trials at sea. Rear Admiral Jim Downey, program manager for the ships, estimates the new delivery date for the Zumwalt will be closer to May 2016.

The Navy is also evaluating the delivery schedules for the remaining two vessels, according to Kent. The Navy and the shipbuilder are executing the test program “with extreme rigor to ensure the highest standards of quality and completeness when the ship sails,” she said.

In an assessment for the Aug. 25 review, Downey wrote that while most management issues with the contractor “are on track,” a pending Bath Iron Works “request for equitable adjustment” for reimbursement of some design, construction and support costs “has strained BIW and Navy management relations.”

The Navy also “continues to witness strained relations between BIW and the labor unions in the shipyard,” he wrote.

Ryan, the General Dynamics spokeswoman, said in e-mail that she wouldn’t comment on such issues.

The new destroyer’s Advanced Gun System from BAE Systems Plc has two 155mm guns capable of firing “precision projectiles” 63 nautical miles (72.5 miles) inland. It’s to carry a crew of 142, down from about 300 on the Navy’s Aegis destroyers and cruisers.

The vessel is larger than any Navy destroyer or cruiser since the nuclear-powered USS Long Beach bought in 1957, according to the Congressional Research Service.