Updated, 6:25 p.m.

The White House sounded a positive note after its first round of deficit-reduction talks with bipartisan, bicameral congressional leaders Thursday, and the group is planning to meet again Tuesday.

“On behalf of all of us, let me say, we had a good, productive first meeting today,” Vice President Biden said in a statement Thursday afternoon, 21 / 2 hours after the talks had begun. “We plan to meet again on Tuesday and look forward to further discussions on these important challenges.”

House Majority Leader Eric Cantor (R-Va.), House Speaker John Boehner’s (R-Ohio) delegate to the talks, told reporters Thursday afternoon that he thought the tone of the talks was constructive and that he was looking forward to next week’s meeting.

“I think this, today, was the first step,” Cantor told reporters in the Speaker’s Lobby after the meeting. “It was a meeting in which I think we had a good rapport develop and I think there needs to be a lot more discussion going forward.”

Participants in the talks, held across the street from the White House at the historic Blair House, included Biden, Cantor, Senate Minority Whip Jon Kyl (R-Ariz.), Senate Appropriations Committee Chairman Daniel Inouye (D-Hawaii), Senate Finance Committee Chairman Max Baucus (D-Mont.), House Budget Committee Ranking Member Chris Van Hollen (D-Md.) and Assistant Democratic Leader James Clyburn (D-S.C.)

According to a pool report of the meeting, Biden cited “two looming concerns” — the debt limit and the “much larger looming issue of the long-term debt” — adding that all parties agree they have to deal with both issues.

The talks come as Congress and the White House are jousting over raising the country’s debt limit, which Treasury Secretary Timothy Geithner has estimated will be reached in August. Republicans are pushing for any debt-limit vote to be linked to a broader deficit-reduction plan, and President Obama last month announced that the White House would host talks with congressional leaders in an effort to draft a bipartisan proposal.

The participants in the talks did not reveal any details on what was specifically was discussed at Thursday’s meeting, and there remains a wide gap between both sides on several key issues: Republicans have maintained that tax increases must not be included in a final deal, while Democrats have blasted Republicans for proposing sweeping changes to federal entitlement programs such as Medicare.

According to a source who was briefed on the talks, representing the White House were Biden, Geithner, Office of Management and Budget Director Jacob Lew, National Economic Council Director Gene Sperling and the council’s principal deputy director, Jason Furman.

Each member of Congress at the meeting was allowed to bring one staffer. At the beginning of the meeting, Biden directed all staff to leave the room for the first 15 minutes according to the source, who was not authorized to speak publicly on the negotiations.

Biden emphasized the parties’ common ground, noting that Republicans want to trim $4 trillion from the deficit over 10 years while Democrats want to cut the same amount over 12 years, the source said.

Both he and Lew said that the administration’s goal was that by 2015, the deficit as a percentage of GDP should be lower than 2.5 percent. They also advocated for a trigger that would ensure that the ratio would not exceed an average of 2.8 percent over the last half of the decade.

Kyl and Cantor, the two Republican negotiators in the talks, said that there would be no way to pass a deficit-reduction plan in the House if it included tax increases. The case they made, according to the source, was that Republicans want to repeal health care but know they will not be able to, and Democrats want to include revenue increases but know that Republicans would oppose that, so both of those options should be taken off the table.

The participants at the meeting also discussed various “trigger” proposals on enacting spending cuts, although nothing was agreed to, sources said. Cantor reiterated his opposition to the notion of a trigger linked to the country’s debt, calling it a “tax trap.”

In addition to the issue of tax increases, there also remains a wide gap on entitlement spending: Republicans have pushed for sweeping changes to programs such as Medicare, while Democrats have publicly blasted the GOP plan.

Even so, Cantor said that there was consensus at the meeting that there are some commonalities among the parties when it comes to spending.

“I think all of us understand that we have got to achieve results, and results mean we’ve got to stop spending money the way this town has been spending money,” he said.

Cantor added that Republicans went to the table Thursday with their 2012 budget blueprint, drafted by Budget Committee Chairman Paul Ryan (R-Wis.), and that Democrats brought the proposal outlined by Obama in a speech last month, which would reduce the deficit by $4 trillion over 12 years.

And he reiterated that even as he and other top Republicans have expressed pessimism about the idea that they’ll be able to reach a deal with Democrats on Medicare, Republicans “have not taken Medicare off the table.”

“What I can say is that this president has done nothing but attack the plan in the budget chairman’s document, and that’s unfortunate, because I think today’s meeting really was in contrast to the rhetoric that we’ve heard before,” Cantor said. “Today’s meeting was one in which we are looking to find commonality.”

Even as the White House negotiations are taking place, another bipartisan group, the Senate’s “Gang of Six,” is also working toward hammering out a deficit-reduction plan, although the group said it was unable to reach agreement on a proposal before Thursday’s talks.