President Obama on Thursday canceled joint military maneuvers between U.S. and Egyptian troops scheduled for next month as he seeks to find levers the U.S. can use to quell deadly clashes in the North African nation and force both sides back into negotiations.

The death toll in Egypt climbed past 600 as the military-appointed government continued its bloody attack on supporters of ousted Islamist President Mohammed Morsi and the Muslim Brotherhood, which vowed to fight until it had defeated the generals. The Brotherhood implored its backers to take to the streets in defiance of a newly imposed state of emergency.

The government, which appears to have set its sights on destroying the political viability of the Brotherhood, said it would intensify its counterattacks and would use live-fire ammunition to fight the protesters.

Scores of Christian churches were attacked, police were gunned down and government buildings in Giza were set ablaze as the violence expanded.

The bloodshed drew condemnation from all sides, and Mr. Obama — taking a short break from his vacation on Martha’s Vineyard — said Egypt is now on “a more dangerous path.”

He said the U.S. no longer will take part in the Bright Star military exercises that American and Egyptian forces conduct every other year.

“While we want to sustain our relationship with Egypt, our traditional cooperation cannot continue as usual,” the president said.

Mr. Obama insisted that the U.S. is not taking sides in the dispute but that the violent clashes cannot go without an American response.

The interim Egyptian government later rebuffed Mr. Obama, warning that his statement, “while it’s not based on facts … can empower the violent militant groups and encourage them in their destabilizing discourse.”

Canceling the military exercises will be seen as a blow to a military that values its close relationship with U.S. forces and gets an annual subsidy of more than $1 billion from Washington. Mr. Obama also said he has asked his advisers to look at other avenues of action.

But the president ducked questions about another step: labeling the military ouster of Mr. Morsi a “coup,” which would require the U.S. to cut off its military assistance to Egypt — a decision the administration would prefer not to make.

Sen. Rand Paul, Kentucky Republican, has been pushing for an end to aid since the beginning of the crisis, and he chastised the administration Thursday for delaying.

“With more than 500 dead and thousands more injured this week alone, chaos only continues to grow in Egypt,” Mr. Paul said in a statement. “So Mr. President, stop skirting the issue, follow the law, and cancel all foreign aid to Egypt.”

Just before Congress fled Washington for a five-week summer vacation, the Senate voted against a Paul proposal to stop military assistance to Egypt, tabling the amendment on a 86-13 vote.

Sen. John McCain, Arizona Republican, also blasted Mr. Obama’s response.

“We violated our own rule of law by not calling it for what it is because our law clearly states that if it’s a military coup, then aid is cut off. So initially we undercut our own values. … That’s a blow to credibility,” He said on CNN.

Mr. Obama said the U.S. understands the “complexity” of Egyptian politics.

“While Mohammed Morsi was elected president in a democratic election, his government was not inclusive and did not respect the views of all Egyptians. We know that many Egyptians, millions of Egyptians, perhaps even a majority of Egyptians, were calling for a change in course,” the president said.

Mr. Obama said that after the military ousted Mr. Morsi in July, there appeared to be a chance for talks and some sort of reconciliation, but the violence moves the dialogue in the wrong direction.

Analysts said canceling the military exercises was a way of distancing the U.S. from the generals in particular. But the move jeopardizes a key pillar of U.S. military-to-military relations, not just with Egypt but with other allies throughout the region.

“You could argue it’s the centerpiece of the U.S.-Egyptian military relationship,” said Jeffrey White, a former senior defense intelligence official, now a fellow at the Washington Institute for Near East Policy.

“There may be a political case [for the cancellation], but it is not a good thing to do from a national security point of view,” said retired Pentagon analyst and veteran Middle East watcher Michael W.S. Ryan, who used to brief Bright Star participants.

The exercise enables senior officers on both sides to get to know each other and work together, said Mr. White, and “keeping those personal relationships is important, especially in the Middle East.”

The exercise, first staged in 1980, is a fruit of the U.S.-brokered 1979 Camp David Peace Accord between Israel and Egypt. It has been held every two years, but the last Bright Star, scheduled for September 2011, was canceled by mutual agreement because of the upheaval in Egypt at the time, said Max Blumenfeld, a spokesman for U.S. Central Command in Tampa, Fla.

This year’s exercise was scheduled to begin Sept. 18 and was to involve just 2,000 U.S. personnel.

Past exercises have involved paratroop assaults, naval maneuvers and bomb disposal scenarios, and have included forces from Britain, France, Germany, Greece, Italy, Jordan, Kuwait, Pakistan and Turkey.

The Egyptian military co-hosts the exercises on an equal footing with U.S. Central Command, which makes it “an important status symbol” for them, Mr. White said.

There are more practical benefits, Mr. Ryan said. “You want to make sure that the first time you’re cooperating [with allies] isn’t when you have people shooting at you for real,” he said.

He said the exercises had to be staged regularly “because personnel on both sides cycle through [to different jobs] over time, and you lose institutional memory. Plus the threats change,” which means the militaries need to be exercising different capabilities.

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