WASHINGTON — A top Republican said more money should be spent to improve diplomatic security after the attack on the U.S. compound in Libya, as Republicans continued their assault of President Barack Obama’s handling of the situation.

“We need to start spending that money and not claim that we don’t have enough money,” Rep. Darrell Issa, chairman of the House oversight committee, said Sunday on CBS’s “Face the Nation.” “If there needs to be supplemental money, of course Congress would respond.”

Republicans have led efforts in recent years to cut federal spending as part of a broader campaign to reduce the size of government, and Congress has repeatedly approved lower levels of funding for the State Department than the White House has sought — though some specific embassy security accounts have been bolstered, aides said.

More money can be made available by tapping unspent funds, Republicans said, or approving a supplemental appropriation, which would require a vote of Congress. Congress is in recess until after the Nov. 6 election.

The top Democrat on the oversight committee, Rep. Elijah Cummings of Maryland, said on the same show that additional money should be made available.

The attacks on the diplomatic mission in Benghazi on the anniversary of the 9-11 attacks killed the U.S. ambassador and three other Americans, and continues to roil the presidential campaign as the White House’s shifting narrative on the event has led to multiple congressional and administration investigations. The White House initially said the attacks grew from anti-American protests over a Californian’s film depiction of the prophet Muhammad, similar to protests in Egypt. But administration officials have since said it was believed to be a terrorist attack.

“Very incompetent or very misleading,” Sen. Lindsey Graham of South Carolina, a top Republican on the Armed Services Committee, said on the same Sunday show.

Obama has held a lead on national security issues over Republican presidential nominee Mitt Romney. But criticisms over the White House’s handling of the Benghazi attack have pushed foreign policy issues back to the forefront.

Republicans sought Sunday to compare Obama’s reaction to the Libya incident to former President George W. Bush’s “Mission Accomplished” declaration — when the Republican president prematurely announced that the main aspects of the Iraq war were finished; violence, in fact, flared and it would be years before the ultimate withdrawal of troops.

“Iraq was falling apart and you couldn’t get the truth from the Bush administration; the Mid-East is falling apart and they’re trying to spin what happened in Libya,” Graham said.

“We’re going through a ‘Mission Accomplished’ moment,” Issa said.

In advance of a congressional hearing last week, former officials said they had warned of security concerns and sought additional funds, but the State Department declined to beef up the security at the embassy in Tripoli.