Defying a veto threat by President Obama, the Senate voted Tuesday to give the U.S. military first crack at holding al Qaeda operatives, even if they are captured in the U.S. and are American citizens, and also reaffirmed the policy of indefinite detention.

“We’re no longer going to have an absurd result that if we capture you overseas where you’re planning an attack on the United States, we can blow you up or put you in a military prison indefinitely, but if you make it to America, all of a sudden you get Miranda rights and you go to federal court,” said Sen. Lindsey Graham, a South Carolina Republican who has fought the Bush and Obama administrations on treatment of suspected terrorist detainees.

Tuesday’s 61-37 vote to buck Mr. Obama and grant the military dibs exposed a deep rift within the Democratic Party. Sixteen Democrats and one independent who caucuses with them defied the veto threat and joined 44 Republicans.

The vote was the latest chapter in a debate that has raged since the Sept. 11, 2001, terrorist attacks plunged the U.S. into the war on terrorism and created the problem of how to handle self-professed enemies who belong to shadowy terrorist groups when they are caught far from traditional battlefields.

In a deal between Armed Services Committee Chairman Carl Levin, Michigan Democrat, and the ranking Republican, Sen. John McCain of Arizona, the military is given custody of anyone who has planned or carried out an attack against the U.S. and its allies, or who is deemed to be a member of al Qaeda or one of its affiliates. The compromise gives the administration the authority to waive military custody but only if top Cabinet officials certify that national security dictates civilian control.

Mr. Obama and his top advisers fought the provisions, arguing that it amounted to micromanaging the war on terrorism. The administration said it should be able to decide on a case-by-case basis whether the military or civilian law enforcement is better able to handle a situation.

“The best method for securing vital intelligence from suspected terrorists varies depending on the facts and circumstances of each case,” Director of National Intelligence James R. Clapper wrote in a letter to senators detailing the administration’s objections.

He said the national security waiver given to the administration still doesn’t allow enough flexibility.

The White House this month threatened to veto the legislation if it “challenges or constrains the president’s critical authorities to collect intelligence, incapacitate dangerous terrorists and protect the nation.” An official on Tuesday said that threat still stands.

The bill also recodifies existing law on indefinite detention and the right of the administration to try suspected terrorists in military commissions rather than civilian courts — authority that the Bush and Obama administrations have exercised, but which Mr. Levin said he wanted to reiterate. Mr. Levin said the administration thought the restatement unnecessary, but didn’t object to the language.

Sen. Mark Udall, Colorado Democrat, tried to strip the detention and the military custody provisions from the bill and replace them with a call for further study of the issue.

“We’re ignoring the advice and the input of the director of the FBI, the director of our intelligence community, the attorney general of the United States,” Mr. Udall said.

His effort won the support of two Republicans, Sens. Rand Paul of Kentucky and Mark Kirk of Illinois, both of whom won their seats in last year’s elections.

Among the Democrats who bucked the administration were members of the Armed Services Committee, and also a host of lawmakers who hold politically vulnerable seats up for election next year. Among them were Sens. Robert P. Casey Jr. of Pennsylvania, Claire McCaskill of Missouri, Robert Menendez of New Jersey, Ben Nelson of Nebraska, Joe Manchin III of West Virginia and Debbie Stabenow of Michigan.

The fight was part of a broader debate over the annual defense policy bill, which is considered one of the few must-pass pieces of legislation Congress considers each year.

After the detainee vote on Tuesday, the Senate rejected an amendment by Mr. Paul that would have ended the grant of authority to go to war in Iraq, which Congress approved in 2002. That amendment was defeated by a vote of 67-30, with four Republicans, 25 Democrats and one independent voting to try to end the war.

With troops already scheduled to be brought home, backers said they wanted to establish Congress’ authority to decide when troops are committed. But opponents said ending the use-of-force authorization might have other unintended consequences for the war on terrorism.

A vote on the overall defense policy bill is expected Thursday. The House has passed its bill, but the two versions will have to be reconciled before the measure goes to the White House, where Mr. Obama’s veto threat will be tested.

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