CNN  — 

President Joe Biden hosted Republican senators for two hours in the Oval Office on Monday afternoon to hear out their proposal for a Covid-19 relief bill drastically less expensive than the $1.9 trillion measure he is pushing.

Afterward, the lawmakers emerged to describe the meeting as “cordial,” “frank” and “useful.” But they did not suggest Biden had come down from his figure, nor did they announce they were willing to meet him at a new number.

“I wouldn’t say that we came together on a package tonight,” Sen. Susan Collins of Maine, who orchestrated the meeting, told reporters afterward. “No one expected that.”

Hours beforehand, the White House had suggested the session was more of a courtesy than a real negotiating opportunity for the new president, who hopes to garner bipartisan support for his first legislative effort.

Biden himself has said he believes relief should pass with or without the support of Republicans. And he has warned against passing a measure that’s too limited given the severity of the dual health and economic crises.

Nevertheless, Biden invited the 10 Republican lawmakers for an early evening session at the White House after they wrote to him requesting his time.

As snow fell outside, Biden and Vice President Kamala Harris sat before a roaring fire in the Oval Office, Collins to his right, to discuss a path forward.

“Thanks for coming down,” he said as the meeting commenced. “I’m anxious for us to talk. I feel like I’m back in the Senate, which I liked the best of everything I did.”

Two hours later, Collins stood outside the West Wing and said Biden had explained some of what was in his bill during their discussion while she and her fellow Republicans outlined their proposal.

“I think it was an excellent meeting, and we’re very appreciate that for his first official meeting in the Oval Office the President spent so much time with us in a frank and useful discussion,” she said, indicating there would be further talks among staffers about a path forward.

In a statement released after the Republicans left 1600 Pennsylvania Avenue, White House press secretary Jen Psaki said the meeting was “substantive and productive” and there were areas of agreement. But Psaki made it clear that if no bipartisan deal is within reach, Democrats going it alone through the process known as reconciliation is a possibility.

“The President also reiterated his view that Congress must respond boldly and urgently, and noted many areas which the Republican senators’ proposal does not address,” Psaki said in the statement. “He reiterated that while he is hopeful that the Rescue Plan can pass with bipartisan support, a reconciliation package is a path to achieve that end. The President also made clear that the American Rescue Plan was carefully designed to meet the stakes of this moment, and any changes in it cannot leave the nation short of its pressing needs.”

Earlier in the day, the White House said the session would not be used to negotiate a new number.

“This meeting is not is a forum for the President to make or accept an offer,” Psaki told reporters during a midday briefing, defending the administration’s figure as necessary to address the crises facing the nation nearly a year into the deadly pandemic.

The message appeared to signal to Democrats and Republicans alike that despite Biden’s professed desire to achieve bipartisan consensus on a relief bill, he remains intent on pressing for his own proposal even as he hears out the views of Republicans.

The 5 p.m. ET meeting with the 10 GOP senators, led by Collins, was Biden’s first publicly disclosed Oval Office session with lawmakers since taking office last month. That it is occurring with Republicans and not Democrats advances the notion he is intent on at least appearing to foster “unity,” the motto of his administration.

Psaki said Monday the session is an example of Biden’s commitment to a bipartisan exchange of ideas.

“He felt it was, you know, an effort to engage and engage on a bipartisan basis, and that’s why he invited them to the White House today,” Psaki said. She sought to emphasize Republican support for a large relief bill by citing interviews West Virginia Gov. Jim Justice gave earlier in the day, including on CNN, when he urged against holding back.

“If we actually throw away some money right now, so what?” the Republican governor said on “Newsroom.”

Psaki said Biden will engage with Democrats in the Oval Office in the future, and emphasized the need to move ahead. He spoke with the two top congressional Democrats, Senate Majority Leader Chuck Schumer and House Speaker Nancy Pelosi, on Sunday.

“It’s incredibly urgent,” Psaki said, citing access to unemployment insurance, food insecurity, and the need for funding for vaccine distributions and public schools.

At the same time, she downplayed the prospects of Biden approving of the Republicans’ bill, which at $618 billion comes in at less than half of Biden’s plan.

“There is obviously a big gap between $600 billion and $1.9 trillion. I don’t believe any of us are mathematicians, but clearly the amount needs to be closer to what he proposed than smaller,” Psaki said during Monday’s press briefing.

The administration is facing a crucial test this week. In addition to the President’s meeting, Democrats are beginning the reconciliation process to potentially pass legislation on their own, which could potentially poison the well for a bipartisan deal.

Many Democrats in Congress believe entertaining Republican counteroffers is merely putting off the inevitable, and would like Biden to proceed quickly to using reconciliation to pass a bill with only a 51-vote majority.

But though he insisted on Friday that Covid relief must pass soon – “no ifs, ands or buts” – Biden remains hopeful of fostering Republican support.

On Sunday, the White House said Biden had spoken to Collins and invited her, along with nine other Republicans, to the White House.

The other invited participants in the meeting are GOP Sens. Bill Cassidy of Louisiana, Shelley Moore Capito of West Virginia, Todd Young of Indiana, Jerry Moran of Kansas, Mike Rounds of South Dakota and Thom Tillis of North Carolina.

The Republicans’ plan places more emphasis on the health effects of the crisis, including by expanding funds for a vaccine rollout. It limits direct payments to Americans and does not include assistance to states and localities, which Democrats have insisted upon as part of any relief measure.

The White House is hoping to move quickly, both to stave off further economic pain and to launch his administration with a legislative win. Certain unemployment benefits also expire soon, lending urgency to the talks.

This story has been updated with additional details from the meeting.

CNN’s Jason Hoffman and Betsy Klein contributed to this report.