Lawmakers on Sunday sharply differed over how the United States should respond to the latest round of violence in Egypt that left hundreds of civilians dead and thousands injured during last week's crackdown by a ruling military that is still being aided by the U.S.

Sen. John McCain, R-Ariz., a leading voice in Congress on foreign affairs, called on the Obama administration to cut off $1.3 billion in annual aid to Egypt, saying the administration's reluctance to do so has weakened U.S. credibility there.

"For us to sit by and watch this happen is a violation of everything that we stood for," said McCain, said on CNN's "State of the Union." "When we threaten something... and then not do it, then you lose your credibility and your influence."

Other lawmakers, however, insisted that continuing aid to Egypt gives the United States greater leverage to bargain with the ruling government on issues like the Suez Canal while also protecting the interests of Israel. Several proposed a compromise in which the aid would continue, but incrementally and only if the Egyptians met stiff demands.

President Obama last week cancelled a planned military exercise with Egyptian forces as violence there escalated between the military and protesting supporters of President Mohammed Morsi, who the military ousted from office. Obama hinted that aid could be cut off if conditions don't improve, but took no immediate steps to do so.

Critics of Obama's approach argue that the ouster of Morsi amounted to a military coup, which under U.S. law would require an immediate halt to all financial aid.

"When they see American tanks on the streets, shooting at people and running over people, do you think that buys us any friendship with the Egyptian people?" Sen. Rand Paul said on Fox News Sunday. "It has to end. It's counter-productive and it shows nothing but American weakness to continue it."

But the administration refuses to classify the military takeover as a coup so that aid can continue to flow, which Sen. Kelly Ayotte, R- N.H., said signals to the military "that whatever they do we will continue our aid."

"I don't see how we can give them aid in light of what has happened," Ayotte said Sunday on NBC's "Meet the Press."

Lawmakers from both parties on Sunday broached a potential compromise, saying the aid could continue to flow into Egypt but only incrementally and with stiff restrictions attached that would help move Egypt toward peace and democracy. Congress will debate future aid to Egypt during budget negotiations next month.

"I think aid will continue to flow after we have this debate this fall," Sen. Bob Corker, the top Republican on the Senate Foreign Relations Committee, said on ABC's "This Week." But "we need to tier it."

"I hope we will continue to have an aid relationship with Egypt," Corker, R-Tenn., said. "I don't want to cut off our relations. I do expect we will have aid forthcoming in a way that really directly focuses on our national interests."

Rep. Pete King, the Republican chairman of the Homeland Security Committee, also supports imposing restrictions on the aid rather than eliminating it.

"I'd be reluctant to cut off aid," King, R-N.Y., said on Fox News Sunday. "We should use it as a bargaining wedge."

The one area of agreement between the lawmakers is that the violence in Egypt must stop.

Sen. Lindsey Graham, R-S.C., who visited Egypt with McCain, called last week's violence "a massacre" that would further destabilize Egypt. That could lead The Muslim Brotherhood, which is fighting the Egyptian forces, to go underground and with help from al Qaeda form an armed insurgency against the Egyptian government.

"We'll have a failed state in Egypt, and we'll have to suspend our aid because we can't support the reaction of the military," Graham said on CBS's "Face the Nation." "That means gas prices go up for us, and the Suez Canal gets compromised and Egypt becomes a staging area for terrorist acts against Israel. This is an absolute disaster in the making."