Updated

Sen. Josh Hawley, R-Mo., said Thursday that he would introduce election integrity legislation, noting that confusion surrounding the 2020 presidential election warranted the need for reform.

"If last 24 hrs have made anything clear, it’s that we need new election integrity laws NOW," he tweeted. "Ban ballot harvesting, guarantee poll watcher access, make ballot counting transparent. I will introduce."

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Hawley's tweets came amid an uproar from President Trump and his campaign over voting methods and how ballots were counted in Tuesday's election. The tight margins in the 2020 presidential election have caused Trump to claim instances potential fraud or error in ballot counts, although no such claims have been substantiated.

Republicans, throughout the election season, have raised concerns about aggregating ballots through "ballot harvesting," as well as the way Republican poll watchers were allegedly deterred at election sites.

Two days after Election Day, neither candidate had amassed the votes needed to win the White House. But Biden’s victories in the Great Lakes states left him at 264, according to the Fox News Decision Desk, meaning he was one battleground state away from becoming president-elect.

As results poured in, Republicans and the Trump campaign filed lawsuits in several states. Judges in Georgia and Michigan quickly dismissed Trump campaign lawsuits there on Thursday.

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Hawley's legislaton would presumably seek to provide some uniformity among a patchwork of state regulations on balloting. The details remain unclear and Hawley's office did not immediately respond to Fox News' request for comment.

Depending on its provisions, the legislation could get stuck in the Senate as Democrats are projected to continue to control the House of Representatives. And more generally, Democrats have opposed restrictions on mail-in balloting.

Meanwhile, the Biden campaign has launched a "fight fund" designed to ensure votes are properly counted. A person familiar with the campaign’s thinking told Fox News that it made this move to be ready to fight all of the Trump campaign’s “meritless legal challenges and shenanigans.”

Members of Trump's team have insisted they have a path to victory while his son, Donald Trump Jr., called out other Republicans for not offering more support.

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"The total lack of action from virtually all of the '2024 GOP hopefuls' is pretty amazing," he tweeted. "They have a perfect platform to show that they’re willing & able to fight but they will cower to the media mob instead. Don’t worry @realDonaldTrump will fight & they can watch as usual!"

After Trump Jr.'s tweet, former U.S. ambassador to the United Nations Nikki Haley tweeted support for the president.

"We all owe @realDonaldTrump for his leadership of conservative victories for Senate, House, & state legislatures," said Haley, who's viewed as a potential contender in 2024. "He and the American people deserve transparency & fairness as the votes are counted. The law must be followed. We have to keep the faith that the truth will prevail."

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Trump Jr. thanked Hawley for his call for reforms, apparently taking a shot at other Republicans. "Thanks @HawleyMO good to see this was before my tweet," he said.

Fox News' Danielle Wallace, Brooke Singman, and the Associated Press contributed to this report.