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Ten Republican senators have agreed to continue talks with the White House in an attempt to negotiate a bipartisan coronavirus relief package, after a two-hour meeting with Joe Biden and Kamala Harris on Monday night ended short of a breakthrough.

The meeting lasted much longer than expected, providing a visible example of the president’s stated ambition to reach across the aisle. But the group of senators who emerged from the Oval Office shortly after 7pm did so empty-handed.

The leader of the Republican pack, Susan Collins of Maine, described the meeting with the president and the vice-president as “excellent”, and “frank and very useful”. But she was clear about the huge gulf that still exists between Biden’s proposed $1.9tn package and the alternative posed by the 10 senators, which is less than a third of that size.

“It was a very good exchange of views,” Collins told reporters as the meeting came to a close. “I wouldn’t say that we came together on a package tonight – no one expected that in a two-hour meeting.”

She added that they did agree to “follow up and talk further on how we can continue to work together on this very important issue”.

After the meeting, the White House put out a statement that bluntly underlined Biden’s unwillingness to allow his relief efforts to be delayed. “While there were areas of agreement, the president reiterated his view that Congress must respond boldly and urgently, and noted many areas which the Republican senators’ proposal does not address.”

The lack of any major advance between the two sides means that Democrats are likely to continue to press ahead quickly with plans to push through Biden’s much larger package without Republican support. Hours earlier, the Senate majority leader, Chuck Schumer, and the House speaker, Nancy Pelosi, filed a joint budget resolution, a step towards passing a relief package without Republican backing.

Susan Collins speaks outside the White House after a meeting with Joe Biden and Kamala Harris. Photograph: Chip Somodevilla/Getty ImagesThat 10 Republican senators were prepared to enter into such a high-profile interaction with Biden and Harris in the first formal meeting held in the Oval Office under the new administration was significant in itself. That is the number who would be needed to vote in favor of any package to reach the 60-vote threshold in the Senate able to resist a filibuster.

The gap between the Democrats’ proposed package and what the Republican senators envision remains enormous – not only is the Republican alternative small by comparison at $618bn, but it contains no funding for state and local governments and differs in other key regards.

The Republican package would offer direct stimulus checks of $1,000 per individual, phasing out for anyone earning above $40,000 a year. By contrast, the Biden plan would offer $1,400 and begin phasing out above $75,000 a year.

Biden’s package is also more generous in extending enhanced unemployment insurance.

Reporters were allowed to witness the start of the Oval Office gathering. Biden and Harris sat on either side of a fire, with Collins on a sofa to Biden’s left and Mitt Romney of Utah to Harris’s right.

The White House made efforts through the day to lower expectations about the discussions. Jen Psaki, the White House press secretary, indicated in the daily press briefing that there was no intention to “make or accept an offer”.

She emphasized that Biden was determined to move swiftly to address the multiple crises posed by the pandemic and its economic consequences. She added: “The president believes that the risk is not going too small, but going not big enough.”

Nine of the senators were physically present at the Oval Office. In addition to Collins and Romney, they included: Lisa Murkowski of Alaska, Todd Young of Indiana, Jerry Moran of Kansas, Thom Tillis of North Carolina, Rob Portman of Ohio, Bill Cassidy of Louisiana and Shelley Moore Capito of West Virginia.

Mike Rounds of South Dakota attended by phone.