Anthony Coscia, the chairman of Amtrak’s board of directors, said on Monday that it was too soon to forecast how much of the repairs could be accomplished during weekends and what impact they would have on train service.

But that work would not lessen the need for new tunnels, which would provide redundancy and increase capacity, he said.

“You sure wish it would go a bit smoother in terms of the funding,” he said. But, he added, “Rest assured, we’re going to take good care of those tunnels.”

Among the challenges Amtrak’s chief executive has to navigate is that other railroads are the biggest users of Amtrak’s infrastructure in and around New York. The Long Island Rail Road and New Jersey Transit carry the bulk of daily users of Penn Station, which New York’s governor, Andrew M. Cuomo, wants to expand by annexing a block of Midtown Manhattan.

Mr. Anderson, a former chief executive of Delta Air Lines, has been Amtrak’s chief executive since 2017, a memorably difficult year at Penn Station. His first day on the job was the third day of what Mr. Cuomo had warned could be a “summer of hell” because of the disruptive emergency track repairs Amtrak undertook.

Mr. Anderson succeeded Charles Moorman, a former chief executive of the Norfolk Southern freight railroad. The two men, each of whom took no salary, shared the chief executive title during a transition that lasted several months as Mr. Anderson learned the railroad business.

By all accounts, Mr. Anderson, who guided Delta through a bankruptcy proceeding, has been successful. Amtrak, which has lost vast sums of money for decades, is expected to report its first operating profit this year.