US president Joe Biden issued one of his strongest condemnations yet of the election fraud claims championed by his predecessor Donald Trump, in a speech decrying Republican efforts to tighten voting rules across the country.

“For those who challenge the results or question the integrity of the election, no other election has ever been held under such scrutiny and such high standards,” Biden said on Tuesday at the National Constitution Center in Philadelphia.

“The big lie is just that: a big lie”, he added, a reference to Trump’s unsubstantiated claim that the 2020 presidential election was stolen from him.

Biden has largely tried to look past Trump during his first months in office. But some Democrats have urged him to take a tougher stance against the former president and his supporters, as Republican lawmakers across the country rally support for tighter restrictions on voting.

“Have you no shame?” Biden asked, in remarks directed at elected Republicans. “Stand up for God’s sake, and help prevent this concerted effort to undermine our election and the sacred right to vote.”

Biden’s speech came one day after Texas Democrats took the bold step of leaving their state’s capital on Monday and flying to Washington.

Their move denied Republicans in the state the two-thirds quorum required to proceed with a vote on a bill to limit ballot access. Greg Abbott, the Republican governor of Texas, has threatened to arrest the fleeing Democrats on their return.

Karine Jean-Pierre, a White House spokesperson, said Biden “applauds [the] courage” of the Texas legislators, who met Kamala Harris, the vice-president, in Washington on Tuesday.

The Texas lawmakers sat down with Chuck Schumer, the Senate’s top Democrat, on Tuesday. They are also expected to meet Joe Manchin, the Democratic West Virginia senator who has opposed changing Senate rules to pass new federal voting rights laws.

Since the 2020 election, Republican lawmakers in statehouses across the US have called for tougher rules on when and how to vote, including a rollback of early voting provisions put in place amid the Covid-19 pandemic.

According to the Brennan Center for Justice, as of mid-May, lawmakers had enacted at least 22 bills to restrict voting in 14 states this year. At least 61 other draft laws in 18 states were being considered by state legislatures. The US justice department has sued the state of Georgia to block a law it passed limiting ballot access, which was condemned by companies including Coca-Cola and Delta.

Biden appealed on Tuesday to the public to support Democrats’ efforts to pass two federal bills to counteract the Republican-led state efforts, “The 21st century Jim Crow assault is real. It’s unrelenting. We are going to challenge it vigorously,” Biden said.

He said that a recent US Supreme Court decision had also put the “burden back on Congress” to act. The court earlier this month rejected claims that two Arizona voting laws — which banned “ballot harvesting” and rejected ballots cast in the wrong precinct — were discriminatory.

Biden and the Democrats face an uphill battle in pushing federal legislation through the Senate, which is split 50-50 between Democrats and Republicans. Senate filibuster rules require most legislation to receive the backing of 60 lawmakers in the 100-member upper chamber.

Several Democratic senators, including Manchin and Arizona’s Kyrsten Sinema, have said they oppose getting rid of the convention to pass voting-related laws.

Jim Clyburn, the South Carolina congressman and longtime Biden supporter, said at the weekend the president “should endorse” the idea of an exemption to the filibuster for voting rights.

Jen Psaki, White House press secretary, told reporters on Monday that Biden remained opposed to eliminating the filibuster. “The filibuster is a legislative process tool . . . but determination about making changes will be made by members of the Senate, not by the president,” she said.

Republicans rejected Biden’s remarks on Tuesday, accusing him of calling for a “federal takeover” of elections, which are administered by state officials.

Lizzie Litzow, a spokesperson for the National Republican Senatorial Committee, said voters “believe in common-sense election security reforms” and accused Democrats of “ignoring the will of the people by stoking false outrage over Republican efforts to make elections more secure”.

A Monmouth University poll conducted last month found 71 per cent of Americans thought in-person early voting should be made easier. At the same time, four in five Americans said they supported laws requiring voters to show photo ID to cast a ballot.