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Senators Chuck Schumer of New York and Richard Blumenthal of Connecticut in May. Mr. Blumenthal was among four senators who announced their support on Tuesday for the Iran nuclear deal, which Mr. Schumer opposes.Credit Michael Appleton for The New York Times

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WASHINGTON — Four Democratic senators announced on Tuesday that they would back President Obama’s nuclear deal with Iran, apparently securing the White House enough votes so Mr. Obama will not be forced to veto a Republican resolution disapproving the accord.

The White House, which had worked aggressively with congressional Democrats to build support for the agreement, had been hoping to avoid the diplomatic embarrassment of Mr. Obama being forced to use his veto to defeat a disapproval resolution.

And as critics in Congress prepared to begin a historic debate on the Iran agreement, the support of the four senators — Richard Blumenthal of Connecticut, Maria Cantwell of Washington, Gary Peters of Michigan and Ron Wyden of Oregon — meant that the Republicans would not have the 60 votes needed to overcome a filibuster of the resolution. Forty-two Democrats now back the agreement.

But while the White House appeared to clinch a victory, Senate Democrats on Tuesday began their own procedural maneuvering. They argued that the Republicans should move immediately to a final vote on the resolution, but one that would require 60 votes for adoption.

Harry Reid Defends Iran Deal

That would spare the Democrats from criticism that they had refused to allow an up-or-down vote on the disapproval resolution, thereby stifling debate on one of the most important foreign policy questions of modern times.

Republican leaders, however, showed no indication that they would give Democrats even the slightest reprieve. The Senate majority leader, Mitch McConnell of Kentucky, among others, has made clear that Mr. Obama and his fellow Democrats would own the nuclear deal and be held accountable in the event of any breaches by Iran. Even many supporters of the accord say they believe cheating by Iran is inevitable.

Ms. Cantwell was the last Democratic senator to announce her position, and she did so in curt remarks to reporters standing in a basement corridor of the Capitol as she arrived to cast a vote on the confirmation of a federal judge.

“I’m for the deal,” she said as she walked quickly to a senators-only elevator, adding that her office would issue a formal statement.

Shortly after Ms. Cantwell’s announcement, Mr. McConnell went to the Senate floor to denounce Democrats for wanting to block the vote and to criticize the accord as deeply flawed.

“The Senate should not hide behind procedure,” Mr. McConnell said. “The American people were led to believe that negotiations with Iran would be about stopping its nuclear program, but that’s not what the deal before us would do.”

For all the drama leading up to this week’s debate, the other five world powers who helped negotiate the agreement — Britain, China, France, Germany and Russia — have made clear they have no desire to return to the bargaining table, and are likely to ease sanctions against Iran and put the agreement in place regardless of the view ultimately expressed by Congress.

Several Democratic lawmakers have cited this reality as a central reason for supporting the accord, so that the United States does not cede its leadership role on the agreement and will remain in a strong position to oversee implementation and enforcement.

So far, Republicans have remained united in their opposition to the agreement, with many saying they are convinced that Iran will not live up to its end of the bargain.

Many Democrats have been torn, particularly in the face of strong opposition by Israel and by some powerful Jewish-American lobbying groups.

On Tuesday, Senator Joe Manchin III of West Virginia became the fourth Senate Democrat to publicly oppose the agreement, joining Benjamin L. Cardin of Maryland, Robert Menendez of New Jersey and Chuck Schumer of New York.

Mr. Manchin, who announced his decision in a conference call with journalists from his home state, said that he was concerned not only with stopping Iran from developing a nuclear bomb, but also with addressing Iran’s support of terrorist organizations. He said the deal failed to do that.

“I have always believed that to truly be a superpower, you must engage in super-diplomacy,” Mr. Manchin said in a statement. “But as I struggled with this decision, I could not ignore the fact that Iran, the country that will benefit most from sanctions being lifted, refuses to change its 36-year history of sponsoring terrorism.”

By not penalizing Iran, Mr. Manchin said, President Obama’s accord “would reward Iran’s 36 years of deplorable behavior and do nothing to prevent its destructive activities.”

“In fact,” he added, “even during the negotiating process, it has continued to hold four Americans hostage, support terrorism around the world, breed anti-American sentiment and acquire arms from Russia.”

The Iran Deal in 200 Words A short overview of highlights from the Iran nuclear pact.