Mr. Trump urged Speaker Paul D. Ryan this week not to support funding for the $30 billion project, two people familiar with the conversation said.
The president's decision to weigh in forcefully against the so-called Gateway infrastructure project, which has been one of the United States' top transportation priorities for years, adds a significant obstacle to getting the project underway in the near future.
Mr. Trump's opposition to the project is in part the result of his belief that it is important to Senator Chuck Schumer of New York, the Democratic leader, according to one person with knowledge of the president's thinking on the issue.
Mr. Trump has told Republicans that it makes no sense to give Mr. Schumer something that he covets — funding for the tunnels — at a time that Mr. Schumer is routinely blocking Mr. Trump's nominees and other parts of his agenda, the person said.
Mr. Schumer could not be reached for comment. News of the president's efforts was first reported by The Washington Post.
The Obama administration, which had ranked the Gateway project the country's No. 1 priority in transportation infrastructure, had informally agreed that the federal government would split the cost of the first phase of the project with New York and New Jersey. That phase was estimated to cost $11 billion, out of about $30 billion for the entire initiative.
Mr. Trump and Mr. Schumer have at times expressed a desire for their parties to work together on a broad effort to rebuild the country's crumbling infrastructure, though there has been little consensus on the details of the projects that would be included and how to pay for them.
In September, Mr. Schumer and Mr. Trump gathered at the White House with other officials — including senators and governors from the region and administration officials — in a meeting that participants described as a productive discussion about ways to make progress on the expensive transportation initiative.
But while both men are New Yorkers and have known each other for decades, they have also become fierce rivals in Washington since Mr. Trump took office last year. And efforts to reach deals on other issues, like immigration, have faltered amid partisan bickering and recrimination.
In recent days, Mr. Trump has grown increasingly angry about Democratic efforts in the Senate, led by Mr. Schumer, to block or delay his nominees to fill key government posts. This week, at the beginning of each news briefing, Sarah Huckabee Sanders, the White House press secretary, began highlighting examples of nominees who had been blocked.
On Thursday, she accused Democrats of blocking efforts to confirm Kevin McAleenan, the president's nominee to lead Customs and Border Protection.
If Mr. Trump succeeds in persuading Republicans to oppose funding the tunnel project, it would be a drastic reversal in fortunes for the region's politicians, who had secured commitments from the president's predecessors.
A spokesman for the Gateway Development Corporation declined on Friday to comment.
This is not the first time that Mr. Trump's administration has signaled that he may not support the Obama administration's agreement.
In December, the acting administrator of the Federal Transit Administration, K. Jane Williams, said in a letter to officials in New York and New Jersey that any such agreement was "nonexistent" and that she had serious concerns about the project.
Ms. Williams said the proposed funding plan would be "a move towards even greater federal dependency."
That response was seen in the New York area as a political maneuver, intended to rewind the negotiations between the federal government and the local sponsors. But it still deflated hopes that the project would maintain its momentum.
The project was meant to supplement the existing tunnels that carry trains under the Hudson River. Those tubes are more than 100 years old and in urgent need of an overhaul after filling with saltwater during Hurricane Sandy in 2012. Elected officials and Amtrak executives have warned that the loss of one of the existing tubes would reduce the capacity for trains between New York and New Jersey by 75 percent and cause chaos for commuters in the region.
In an interview this week, Rick Cotton, the executive director of the Port Authority of New York and New Jersey, called Gateway "the most pressing infrastructure project in the country at the moment."
He added that "any national infrastructure program worthy of the name could not possibly fail to provide significant funding for Gateway."
If it gets built, the project includes the replacement of a rail bridge in northern New Jersey that is a contemporary of the existing tunnels and improvements at Pennsylvania Station in Manhattan. Officials at Amtrak, which owns Penn Station and the existing tunnels, have been pressing for it for years since former Gov. Chris Christie of New Jersey canceled a different project, which was known as the ARC tunnel.
The ARC project, sponsored by New Jersey Transit, the state-run operator of commuter trains and buses, involved digging a new tunnel that would carry trains to a new station deep below 34th Street in Midtown Manhattan. Construction had already begun on that project when Mr. Christie, a Republican who endorsed Mr. Trump for president, halted it in 2010.
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