Republicans in the Senate blocked a measure on Wednesday that would bar President Trump from using military force against boats in the Caribbean Sea, turning back an effort to check his power to wage war without authorization from Congress.

The vote against bringing up the Democratic resolution was 51 to 48, mostly along party lines. It came less than a week after the U.S. military carried out the fourth strike in the Trump administration’s legally disputed campaign targeting alleged drug runners in the Caribbean.

Senators Adam Schiff of California and Tim Kaine of Virginia, both Democrats, tried to force action on the measure, invoking a provision of the 1973 War Powers Act, which requires that resolutions to terminate hostilities be considered under expedited procedures.

They said they were doing so in response to the series of strikes Mr. Trump has carried out since Sept. 2, which the administration says have killed 21 people. The White House has described the strikes as part of a campaign against Venezuelan drug cartels that it accuses of smuggling fentanyl into the United States.

“This is the kind of thing that leads the country unexpectedly and unintentionally into war,” Mr. Schiff said ahead of Wednesday’s vote. He said the resolution also sought to limit the president’s ability to expand his campaign beyond striking boats.

That was a direct response to the White House decision a day earlier to end efforts to reach a diplomatic agreement with Venezuela, a possible signal that the administration was considering escalating its campaign to stronger measures more directly targeting the government of President Nicolás Maduro.

The series of strikes on vessels has drawn criticism from both Democrats and Republicans on Capitol Hill, including Senators Lisa Murkowski of Alaska and Rand Paul of Kentucky, the only two Republicans who voted with nearly all Democrats in favor of limiting the president’s authority.

Mr. Paul, who opposes American military intervention abroad, said he was dissatisfied with the administration’s justification for the strikes and questioned why the boats were not intercepted. He argued that attacking them left too much uncertainty about who was on board and whether they were carrying drugs.

“If anyone gave a you-know-what about justice, perhaps those in charge of deciding whom to kill might let us know their names, present proof of their guilt and show evidence of their crimes,” Mr. Paul said.

Ms. Murkowski noted that the Trump administration’s approach to curbing the presence of drugs into the country still needed congressional input.

“We all want to get rid of the drugs in this country, absolutely,” she said. “But the approach that the administration is taking is new, some would say novel, and I think we have a role here.”

Last week in a letter to Congress, the administration said that Mr. Trump had “determined” that the United States was engaged in a formal armed conflict with certain drug cartels his administration has deemed terrorists. The notice did not name the specific groups involved.

The justification was criticized as inadequate by some, but since the first strike, some of the president’s Republican allies on Capitol Hill have sought ways to grant the administration more formal authority to continue carrying out such strikes. They have privately discussed authorizing a broad use of military force against drug cartels that Mr. Trump deems to be “terrorists,” as well as against any nation that he says has harbored or aided them, according to people familiar with the matter.

“This is an attack on the United States by people who have been designated as terrorists,” said Senator James E. Risch, Republican of Idaho and chairman of the Senate Foreign Relations Committee, speaking against the resolution. “The president not only has the right, he has the duty to do something about this.”

Last month, Mr. Kaine, along with 23 other Democrats in the Senate, sent a letter to the White House questioning the legal basis for the first military strike conducted on Sept. 2. He said that the letter had gone unanswered and that the justifications given in notices to Congress and classified briefings had been inadequate.

“We asked basic questions: Give us the intel about these particular boats, that they’re actually carrying narcotics. Tell us why you decided in these cases not to interdict but to strike,” Mr. Kaine said. “These are really important questions. They’re questions that an administration should respond to Congress about. We asked for a response within a week. We’ve not gotten answers to these questions.”

Senate Republicans, who maintain a 53-to-47 majority, have successfully defeated similar attempts to limit Mr. Trump’s authority to wage war against foreign adversaries.

In June, senators voted mostly along party lines to defeat a measure that would have required that the president first seek congressional approval before carrying out additional strikes against Iran. The vote came just days after the U.S. military conducted Operation Midnight Hammer, in which the president directed forces from both the Air Force and the Navy to carry out strikes against three nuclear facilities in Iran.

Mr. Paul was the sole Republican to break with his party to vote in favor of placing more limits on the president in that case. Senator John Fetterman of Pennsylvania, an outspoken supporter of Israel who said at the time that the strikes were necessary, was the only Democrat to oppose it.

He again broke with his party on Wednesday and rejected the efforts to rein in Mr. Trump’s attacks in the Caribbean by opposing the resolution.

Republicans supporting the president’s campaign maintain that he is operating within the bounds of his constitutional authority as commander in chief, an assertion that past presidents of both parties have relied on when carrying out a variety of military strikes without consulting Congress.

“This looks to me like an area that’s pretty squarely within Article II,” Senator Josh Hawley, Republican of Missouri, said, referring to the portion of the Constitution that lays out the president’s powers as commander in chief of the U.S. military. The Trump administration has contended that bringing illicit drugs to American shores qualifies as an imminent threat to national security, giving the president inherent authority to use military force to counteract it.

Mr. Kaine and other Democrats have long hoped that Republicans who often express frustration behind closed doors about Mr. Trump’s unchecked exercises of power will eventually go public with their disapproval.

That was the case in April when Mr. Kaine successfully attracted a handful of Republican votes for his effort to cancel some of the Canadian tariffs Mr. Trump had imposed. But in the months since, it has proved to be an isolated move and has done little to curtail his aggressive tariff strategy.

“Having talked to a great many of my Republican colleagues, I think it’s fair to say there is bipartisan concern over these administration actions using lethal force this way,” Mr. Schiff said.

In the end, though, all but two Republicans voted against the war powers measure on Wednesday.

Megan Mineiro contributed reporting.