A crush of rail delays in July brought renewed attention to an Amtrak proposal to build a new tunnel as part of what is known as the Gateway project. After Mr. Foxx urged the states to make the project a priority, the governors sent the letter to President Obama in September saying if the federal government provided grants for half the costs, the states would cover the balance.

The flurry of activity amounted to the most progress on the issue since 2010, when Mr. Christie canceled another tunnel proposal. Still, major questions have yet to be answered:

How would the states pay for their share when leaders are already struggling to fund existing infrastructure plans? Could Congress, already wracked by leadership questions, be persuaded to provide significant federal funding? And would the Port Authority, shadowed by scandal and a continuing federal investigation, be the best agency to oversee one of the biggest construction projects in the country?

But transportation and business officials said the initial steps that Mr. Foxx outlined were significant. Local leaders at the speech were enthusiastic about the developments, said Kathryn S. Wylde, president of the Partnership for New York City, which hosted the breakfast where Mr. Foxx spoke.

“From our standpoint, the most important message was that the project is moving forward on an accelerated basis,” Ms. Wylde said, “and there is consensus that the federal and state governments are going to work together to make sure we have the resources to deal with what we certainly think is an infrastructure emergency.”

As part of the planning process, New Jersey Transit has agreed to give Amtrak its studies from the earlier tunnel proposal, known as Access to the Region’s Core. Amtrak has also been working to preserve the right of way for the future tunnel at the Hudson Yards site in Manhattan. Amtrak has asked New Jersey Transit and the Metropolitan Transportation Authority to pay about $5.5 million each toward the work there, Amtrak officials said.

On Thursday, Mr. Foxx said that the environmental and engineering work were necessary preliminary steps so officials could determine the scope and cost of the project before they figure out the details over funding. He said that he would try to make the funding framework proposed by the governors work, but that it would require a strong push from the region’s congressional delegation.

The Gateway proposal, which includes a new two-tube rail tunnel, an expanded Pennsylvania Station, a replacement for the Portal Bridge in New Jersey and other upgrades, could happen in phases, Mr. Foxx said, with the new tunnel being the first priority.