A federal judge has reversed a freeze put on funds by Donald Trump for $16bn in enhanced rail links connecting New York and New Jersey amid reports that the US president wants major travel landmarks named after him in return for continued investment.

The Gateway Project will build a new commuter rail tunnel between Manhattan and New Jersey under the Hudson River on the western side of New York City and repair a century-old tunnel used by more than 200,000 travelers and 425 trains daily.

The existing River tunnel was heavily damaged by Hurricane Sandy in 2012 and needs frequent emergency repairs that disrupt travel on the nation’s most heavily used passenger rail line.

US district judge Jeannette Vargas in New York on Friday handed down the temporary ruling hours after New York and New Jersey authorities said construction would halt for lack of funding.

Vargas said the states were likely to succeed on their claims that a Trump administration directive freezing the funds was arbitrary and ran afoul of legal procedures for making policy changes.

The White House and the US Department of Transportation did not immediately respond to requests for comment on the ruling.

New Jersey’s acting attorney general, Jennifer Davenport, and New York’s attorney general, Letitia James, issued statements praising the ruling.

“The Trump administration must drop this campaign of political retribution immediately and must allow work on this vital infrastructure project to continue,” Davenport said.

The two states said in a 3 January lawsuit that the Trump’s Republican administration had frozen the funds in a “brazen act of political retribution” against their Democratic leaders. They said a work stoppage would hold up a crucial infrastructure project, damage their economies and saddle them with costs from securing idled construction sites.

The Trump administration has withheld $205m in reimbursements for the project since 1 October. Trump has reportedly demanded that the Washington Dulles international airport and New York’s Penn Station be renamed for him in exchange for unfreezing the funds, drawing strong criticism from Democrats.

He told reporters on Friday that he had not proposed renaming Dulles or Penn Station. Trump did not comment on Vargas’s decision.

The US Department of Transportation said on 30 September that it froze the funds pending a review of the project’s compliance with new federal prohibitions against race- and sex-based considerations in contracting decisions.

The Gateway Development Commission informed the department that it had made changes and conducted a review to ensure compliance with the regulations but has not heard back, according to the lawsuit.

Gateway said the suspension would idle 1,000 construction workers and that Trump’s decision had endangered passengers who had to rely on “decaying, century-old rail infrastructure”. Gateway had previously said work was already suspended.

Trump last month asked Chuck Schumer, the minority leader of the US Senate, to back the renaming of the Washington Dulles international airport and Penn Station after the president. Trump told reporters on Friday that Schumer had proposed renaming Penn Station, but Schumer, who represents New York, called the claim an “absolute lie” in a social media post.

Cory Booker, the senator from New Jersey, said Trump was holding the tunnel hostage, while the New York senator Kirsten Gillibrand, a fellow Democrat, said the president “continues to put his own narcissism” over the projects’s union jobs and economic benefits.

Reuters contributed reporting