WASHINGTON — Senate Republicans revived negotiations Tuesday over President Joe Biden’s sweeping investment plan, preparing a $1 trillion infrastructure proposal that would be funded with COVID-19 relief money as a counteroffer to the White House ahead of a Memorial Day deadline toward a bipartisan deal.

The Republicans said they would disclose details of the new offer by Thursday, sounding upbeat after both sides had panned other offers.

At the White House, press secretary Jen Psaki declined to address the new plan, but said: “We expect this week to be a week of progress.”

Talks over the infrastructure investment are at a crossroads as Biden reaches for a top legislative priority. The White House is assessing whether the president can strike a bipartisan deal with Republicans on his American Jobs Plan or whether he will try to go it alone with Democrats if no progress is made in the days ahead.

Yet the administration and the GOP senators remain far apart over the size and scope of the investment needed to reboot the nation’s roads, bridges and broadband — but also, as Biden sees it, the child care centers and green energy investments needed for a 21st-century economy. They also can’t agree on how to pay for it.

Biden had dropped his $2.3 trillion opening bid to $1.7 trillion, and Republicans had nudged their initial $568 billion offer up by about $50 billion late last week, but talks teetered as both sides complained the movement was insufficient.

The Republicans have uniformly rejected Biden’s plan to pay for the investments by raising the corporate tax rate, from 21% to 28%. Instead, the GOP senators want to shift unspent COVID-19 relief funds to infrastructure, which may be a nonstarter for Democrats. Republicans also want to rely on gas taxes, tolls and other fees charged to drivers to pay for the highways and other infrastructure.

The Republicans said their new proposal would be aligned with what they discussed with Biden in their first Oval Office meeting almost two weeks ago.

“We are anxious to have a bipartisan agreement,” said Sen. Shelley Moore Capito, R-W.Va., who is leading the group of GOP negotiators.

A GOP aide who spoke on condition of anonymity to discuss the private talks said the price tag would be $1 trillion over eight years, paid for by tapping funds that have been allocated as part of COVID-19 relief but not yet spent. The aide said about $700 billion remains in unspent virus aid.

Psaki declined to comment on the forthcoming GOP proposal, but Democrats on Capitol Hill were quick to rebuff dipping into coronavirus relief funds, particularly money that had been sent to the states and local governments that now seems less urgent as some jurisdictions reported better-than-expected balance sheets.