WASHINGTON (Reuters) - Democrats in the U.S. Congress pledged on Monday to intensify pressure for stricter gun-sale background check legislation, citing strong public backing for the measure, but received no sign of support yet from President Donald Trump.

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With Congress returning from a long summer recess, Senate Minority Leader Chuck Schumer and House of Representatives Speaker Nancy Pelosi again urged the Republican-controlled Senate to promptly approve a bill clamping down on unregulated gun sales through the internet and at gun shows.

“We are not taking no for an answer,” Pelosi told a news conference in which Schumer said approving the House-passed background check bill should be “our first order of business.”

The calls for gun legislation grew last month following mass shootings in the Texas cities of El Paso, Odessa and Midland, and in Dayton, Ohio.

But Senate Majority Leader Mitch McConnell opened the Senate’s autumn work session without mentioning gun legislation.

In remarks to reporters at the White House, Trump said he was “dealing” with Republicans and Democrats on gun control. “At the same time, we have to protect our Second Amendment very strongly and we will always do that,” he added, referring to the U.S. Constitution provision guaranteeing a right to bear arms.

Amid the recent mass shootings, McConnell said he would not bring a gun bill to the floor of the Senate unless it had Trump’s support.

Democratic Senator Chris Murphy, a leading gun control advocate, issued a statement on Monday saying that “time is running short” to strike a deal on a background check bill that could pass Congress. He added: “It seems more likely that we’re going to find ourselves back in a familiar place where 90 percent of the Americans who want more background checks are going to be disappointed once again.”

Dayton Mayor Nan Whaley, who spoke at the Pelosi-Schumer news conference, said she was in Washington demanding “a simple vote on what nine out of 10 Americans agree on. I don’t know of anything else that nine out of 10 Americans agree on except HR 8,” referring to the House’s background check bill.

A bipartisan group of mayors met with high-ranking White House officials earlier on Monday to discuss gun legislation but gave no indication of an agreement between the two sides.

Trump has said he favored action, possibly on tackling mental health issues related to gun violence or expanded background checks. The White House has yet to outline any specific proposals.

Bryan Barnett, mayor of Rochester Hills, Michigan, and the current head of the U.S. Conference of Mayors, said there was a “robust” discussion about gun legislation at the White House. He said the White House team talked about “a suite of solutions” and that background checks “are certainly on the table.”

White House officials said last week the measures might include expediting the death penalty for mass shooters.