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In an effort to dispute what they say is a false narrative that union voters are closely split between Hillary Clinton and Senator Bernie Sanders of Vermont, a group of more than 20 unions representing more than 10 million workers released a statement on Monday reaffirming support for Mrs. Clinton.

“Secretary Clinton has proven herself as the fighter and champion working people and their families need in the White House,” says the statement, which was embraced by several large unions, including the American Federation of State, County, and Municipal Employees, the American Federation of Teachers, and the Service Employees International Union. “That is why, of all unions endorsing a candidate in the Democratic primary, the vast majority of the membership in these unions has endorsed her.”

The statement is partly a reaction to the aftermath of the announcement by the A.F.L.-C.I.O., a federation of unions, that it would not vote during its executive council meeting this week on whether to endorse a candidate in the Democratic presidential primaries, essentially postponing an endorsement until the primaries are no longer competitive.

“I have concluded that there is broad consensus for the A.F.L.-C.I.O. to remain neutral in the presidential primaries for the time being,” Richard L. Trumka, the A.F.L.-C.I.O. president, said in an email to union officials last week.

Supporters of Mr. Sanders argued that the decision not to hold an endorsement vote reflected substantial enthusiasm for him among rank and file union voters, even within unions that had already endorsed Mrs. Clinton.

“I would say over all that union members are divided,” said Larry Cohen, a senior adviser to Mr. Sanders and past president of the Communications Workers of America.

“It’s significant given where we were last spring that we’re now at a point that the A.F.L.-C.I.O. is not coordinating a campaign in the primaries, that the A.F.L.-C.I.O. would essentially be encouraging members to be active for whichever candidate they support.”

But leaders of prominent unions backing Mrs. Clinton say this is a misreading of the federation’s decision. “The A.F.L.-C.I.O. virtually never endorses in primaries,” said Randi Weingarten, the president of the 1.6-million member American Federation of Teachers.

“Because there’s now a story where there should not have been one — certain people in the Bernie camp wanted to take advantage of it — the unions that endorsed Hillary want to make really clear to people that we are incredibly supportive of her.”

The A.F.L.-C.I.O. endorsed Vice President Al Gore in October 1999, shortly before he competed against former Senator Bill Bradley in the 2000 Democratic primaries. It endorsed Senator John Kerry in February 2004, after Mr. Kerry had piled up victories in more than a dozen contests, including the Iowa caucuses and the New Hampshire primary, and appeared on his way to the nomination though he still faced a challenge from Senator John Edwards. (Mr. Edwards finished unexpectedly close to Mr. Kerry in the Wisconsin primary shortly before the federation’s endorsement that year.)

In 2008, the A.F.L.-C.I.O. did not endorse a Democratic candidate — Barack Obama — until June, by which point Mr. Obama had already effectively captured the nomination over Mrs. Clinton.

To win an endorsement, a candidate must get the support of unions representing at least two-thirds of the federation’s 9.3 million members. Mrs. Clinton was roughly one million votes shy of this total at the time the federation decided to abandon the process last week, according to two sources briefed on the decision.

In addition to the problem of basic math, these sources said, at least one president of a major union supporting Mrs. Clinton urged aborting the process out of fear that pushing forward with a vote could be divisive. Others worried that a vote could divide the labor movement more broadly.

“I do believe it would not be beneficial to push the issue,” said Lee Saunders, president of the 1.6-million member American Federation of State, County, and Municipal Employees, or Afscme, which has also endorsed Mrs. Clinton and was part of the joint statement. “Everyone will have to come together when there’s a Democratic candidate.”

In truth, both sides have evidence to back up their claims about the state of the race among union voters. Mrs. Clinton has the endorsement of 23 unions, versus three for Mr. Sanders, and the unions that have endorsed her represent more members than all the unions in the A.F.L.-C.I.O. (Some large unions, like the two-million member Service Employees International Union, are not part of the federation.)

Exit and entrance polls from the Iowa and Nevada caucuses showed voters from union households favoring Mrs. Clinton over Mrs. Sanders by a roughly 10-point margin — greater than the margin by which Mrs. Clinton won those contests overall.

Still, that 10-point margin — assuming it is correct, which is not necessarily assured — may reflect a narrowing of the gap between the two candidates among union members since last fall. In the three polls that Afscme conducted between last May and October, more than 60 percent of its Democratic members consistently backed Mrs. Clinton, versus no more than 20 percent who backed Mr. Sanders.

It is impossible to know the margins by which members of specific unions voted for Mrs. Clinton in this year’s early primary contests, but other evidence suggests significant pockets of support for Mr. Sanders. The Afscme council in Washington State endorsed him in January, and a prominent service employees union local in New Hampshire endorsed him in November.

Ms. Weingarten suggested that some of the blame for confusion about the level of labor support for Mrs. Clinton resided with the A.F.L.-C.I.O., which she said had given the impression that a Clinton endorsement might be imminent in the run-up to this week’s meeting, and to a similar meeting last summer.

She pointed out that many unions were increasingly forming ad hoc alliances outside the federation to work on key issues, like pensions and the ability of unions to collect fees from nonmembers.

“The traditional role the A.F.L. is supposed to have is marshaling all this energy, and they’re not doing it, we’re doing it ourselves,” she said. “This in some ways is just more of that. Frankly I’m surprised the A.F.L. put itself in position, both in July and now, where they were creating an expectation that was never there.”