WASHINGTON — To hear the participants tell it, President Biden’s first-ever meeting with Republican and Democratic leaders from both houses of Congress was 90 minutes of productive conversation. It was cordial. There were no explosions of anger.

But the agreeable tenor could barely mask the legislative reality: The two parties remain deeply divided over the president’s proposal for $2.3 trillion in spending to upgrade the nation’s crumbling infrastructure.

The meeting produced only minuscule progress on Mr. Biden’s ambitious efforts to invest more broadly in the United States than at any time in generations, underscoring the political challenge for the president as he seeks to exploit the narrowest of majorities in Congress to revive and reshape the country’s economy.

“It was different than other meetings,” marveled Representative Kevin McCarthy of California, the House Republican leader and a veteran of chaotic White House meetings with President Donald J. Trump. “Everybody was pleasant.”

Speaking in front of the West Wing shortly after leaving the Oval Office, Mr. McCarthy and Senator Mitch McConnell of Kentucky, the Senate Republican leader, said they had agreed with Democrats on the need to settle on what constitutes infrastructure in the first place.

But even on that very minor point, there appeared to have been little movement.

“We first have to start with a definition of what is infrastructure,” Mr. McCarthy told reporters before repeating Republican talking points about Democratic efforts to define infrastructure too broadly. “That’s not home health. That’s roads, bridges, highways, airports, broadband.”

Republicans have balked at the president’s $2.3 trillion “American Jobs Plan,” which would vastly increase spending on home health aides, colleges and broadband as well as more traditional infrastructure targets like roads and bridges. Republican lawmakers have said that there should be less spending overall and that they oppose tax increases to pay for it.

The meeting on Wednesday included Mr. McCarthy and Mr. McConnell, as well as their Democratic counterparts, Senator Chuck Schumer of New York and Speaker Nancy Pelosi of California. Vice President Kamala Harris also participated.

Since taking office, the president has barely talked with Mr. McCarthy, who voted on Jan. 6 to overturn Mr. Biden’s 2020 election victory in key battleground states. Asked afterward about the election, Mr. McCarthy sought to play down the issue.

“I don’t think anybody is questioning the legitimacy of the presidential election,” Mr. McCarthy said. “I think that is all over with.”

That is not true. Mr. Trump continues on a near daily basis to insist, contrary to fact, that the election was corrupt and stolen from him. And only hours before the discussion at the White House on Wednesday, Mr. McCarthy himself led the charge to oust Representative Liz Cheney of Wyoming from her position as the No. 3 Republican in House leadership because she refused to drop her public criticisms of the former president and her party for the election falsehoods.

The closed-door meeting at the White House was part of Mr. Biden’s attempt to live up to his campaign promise to seek bipartisan agreement on major policy proposals. He pushed through his first legislative achievement, a $1.9 trillion stimulus bill, by using a legislative maneuver that allowed it to pass with only Democratic votes.

As the group assembled in the Oval Office, the president told reporters that he hoped to find common ground, at least on infrastructure spending. He joked that he would like to just “snap my fingers” to achieve that goal despite fierce Republican opposition to his plans.

“The bottom line here is we’re going to see whether we can reach some consensus on a compromise,” Mr. Biden said. “We’re going to talk a lot about infrastructure.”

The Republican lawmakers said that they believed the meeting was productive.

Mr. McConnell told reporters after the meeting that he hoped Senate committees would handle the president’s proposals through the normal legislative process, which could increase the chances of a deal. Mr. Biden is scheduled to meet on Thursday with Senator Shelley Moore Capito, Republican of West Virginia, who has taken on the role of lead negotiator for Senate Republicans.

Returning to the Capitol, Democratic leaders framed the meeting as a modest sign of progress.

“It took us a few steps forward,” Ms. Pelosi said. Her Senate counterpart, Mr. Schumer, said that the two parties would “try hard” to get an agreement, taking the “first step” to identify potential areas of common interest.

But it is unclear whether the two sides can agree on enough even to break up the infrastructure plan into two bills: one narrower traditional infrastructure measure that could potentially win bipartisan support, and a larger jobs and tax bill that Mr. Biden might try to push through Congress with only Democrats.

The Republican leaders said they remained unwilling to consider any of the tax increases that Mr. Biden has suggested to pay for the spending.

“You won’t find any Republicans going to go raise taxes,” Mr. McCarthy said, referring to Mr. Biden’s desire to increase taxes on wealthy Americans that were lowered in the 2017 tax bill. “I think it’s the worst thing to do in this economy.”

He and Mr. McConnell also said that their membership remained at odds with the president about how to define infrastructure spending. At one point, Mr. Biden and Democrats pressed their Republican counterparts on a specific proposal to fund a vast network of charging stations for electric cars, but they showed little interest.

“We didn’t go through a list and say, ‘Yes on this, no on that,’” Ms. Pelosi said afterward. “But that emerged as something that they might not be too fond of.”

Mr. Biden and Ms. Harris have toured the country in recent weeks arguing that the spending is necessary to create jobs and ensure that the economic recovery from one of the nation’s deepest recessions does not lose momentum. They have defended the infrastructure proposal from criticism that it includes too much spending on social services programs unrelated to the traditional road-rail-and-sewer definition of infrastructure.

And the differences between the two parties are even starker for Mr. Biden’s second legislative proposal: the $1.8 trillion “American Families Plan,” which seeks to expand access to education, reduce the cost of child care and support women in the work force.

The meeting on Wednesday comes less than a week after a disappointing jobs report, which showed only 266,000 new jobs added in April. Republicans pointed to the data point as proof that Mr. Biden’s policies were creating a labor shortage and that his spending proposals threatened to stoke runaway inflation.

A White House statement after the meeting stressed the president’s desire to avoid partisan clashes that could prevent the United States from taking steps to improve the economy.

“The president also emphasized that whatever differences exist between the parties, the real competition is between the United States and the rest of the world, and that other countries are not waiting for us to equip our people to win in the 21st century,” the statement said.

But the Republican leaders made no secret of their intention to fiercely oppose Mr. Biden’s plans if he tries to go around them. In remarks on the Senate floor before the meeting, Mr. McConnell said Democrats should remember they have only a narrow majority in Congress, “not exactly a sweeping mandate for a socialist agenda.”

And in a campaign text to supporters shortly after the meeting, Mr. McCarthy sought to raise money by saying, “I just met with Corrupt Joe Biden and he’s STILL planning to push his radical Socialist agenda onto the American people.”