The White House on Thursday welcomed the $928 billion Republican counteroffer on infrastructure as “constructive” and signaled bipartisan talks would continue into next week as President Biden pressed for swift action.

“At first review, we note several constructive additions to the group’s previous proposals, including on roads, bridges and rail,” White House press secretary Jen Psaki said in a statement Thursday. “At the same time, we remain concerned that their plan still provides no substantial new funds for critical job-creating needs, such as fixing our veterans’ hospitals, building modern rail systems, repairing our transit systems, removing dangerous lead pipes, and powering America’s leadership in a job-creating clean energy economy, among other things.”

Biden phoned Sen. Shelley Moore Capito (R-W.Va.) on Thursday to thank her for the counterproposal, Psaki said, and White House staff are expected to continue to engage with officials on Capitol Hill next week on a potential deal.

Biden stressed to reporters at Joint Base Andrews that he needed to get infrastructure done “very soon” and said he planned to meet with Capito next week, while Congress is on recess. Biden also indicated he would speak to another Republican group that is working on an alternative on infrastructure.

“I had a good conversation, very brief, but a good conversation with Capito … I told her we have to finish this very soon,” he told reporters before departing for a trip to Cleveland, Ohio. “We’re going to have to close this down soon.”

The Republican offer unveiled Thursday is significantly higher than their original proposal but still falls far short of the $1.7 trillion offer that the White House outlined last week. Lawmakers on both sides of the aisle have been skeptical about the possibility for bipartisan compromise.

Still, the developments make clear that bipartisan negotiations will continue at least for another week, despite the White House saying it expected to see progress on a bill by Memorial Day, which is Monday. Psaki reiterated Thursday that Biden would like to have an infrastructure bill passed by summer – an aggressive timeline.

The White House also expressed concerns about Republicans’ proposal to repurpose unspent funds from Biden’s $1.9 trillion coronavirus relief plan in order to pay for the infrastructure investments, underscoring the enduring sticking point between the White House and GOP on how to pay for the package. 

“We are worried that major cuts in COVID relief funds could imperil pending aid to small businesses, restaurants and rural hospitals using this money to get back on their feet after the crush of the pandemic,” Psaki said. 

The Republicans on Thursday proposed paying for the package through a combination of unspent coronavirus relief funds, user fees and infrastructure financing. The White House has already opposed user fees as a payment method, saying they would violate Biden’s pledge not to raise taxes on those making less than $400,000 per year.

Speaking to reporters on Air Force One, Psaki wouldn’t call using the coronavirus funds as a nonstarter but said the White House believes “there are better ways to pay for it.”

According to the White House, roughly 95 percent of the coronavirus relief money approved by Congress before Biden's rescue plan had been obligated or intended for small business assistance, unemployment insurance or nutrition assistance as of the end of March. Of the remaining 5 percent that is unobligated, most of the funding is meant for rural hospitals, health care providers and small business disaster loans. The White House has not specified how much of Biden's American Rescue Plan has been obligated.

Biden has proposed paying for a package by raising the corporate tax rate. Republicans have opposed that and other proposed tax increases on the wealthy that would undo the 2017 Trump tax cuts.

The decision to continue negotiations with Republicans may rankle some Democrats who would like to see Biden ditch the negotiations and pursue a large package using budget reconciliation.  

Speaking on MSNBC, Sen. Elizabeth Warren (D-Mass.) said she didn’t believe the GOP proposal to be a “serious counter offer.” Warren took issue with the Republican plan to pay for the proposal and the lack of investment in green technology while arguing their proposal does not do enough to help women in the workforce.

Psaki would not specify when the White House would decide whether or not to abandon talks with Republicans but said officials “look forward to making progress” before Congress returns to Washington on June 7. 

Updated at 2:10 p.m.