The New York mayor, Bill de Blasio, has stepped up his campaign for increased federal funding for US cities during the coronavirus crisis, asking Donald Trump whether his administration was “going to save New York City or are you telling New York City to drop dead?”

De Blasio’s dramatic language came during his press conference on Sunday, after he warned last week that he planned to cut a further $2bn from the city’s municipal services budget due to the economic downturn. He said the city was likely to lose at least $7.4bn in tax revenue over the current and next fiscal year.

De Blasio has criticized the $2tn coronavirus relief package that Trump signed last month, saying New York only received $1.4bn from the stimulus, compared with around $58bn for the airline industry. He has called for the next package, which congressional and administration leaders say they are “close” to reaching a deal on, to include tens of billions for states, cities and municipalities.

The mayor had harsh words for the president, claiming both he and the vice-president, Mike Pence, have ignored his overtures on the stimulus funds.

On Sunday, De Blasio sent a message to the administration that echoed a New York newspaper headline during the city’s bankruptcy crisis of the 1970s.

“There was that famous Daily News cover that said ‘Ford to City: Drop Dead,’” De Blasio said. “So my question is, Mr Trump, Mr President, are you going to save New York City or are you telling New York City to drop dead? Which one is it?”

“President Trump, what’s going on? Cat got your tongue?” De Blasio continued. “You’re usually really talkative. You usually have an opinion on everything. How on earth do you not have an opinion on aid to American cities and states?”

The Daily News front page was published after Gerald Ford gave a speech in 1975, saying he would veto a federal bill that would have helped spare New York City from bankruptcy.

Across many US cities and states the issue of budget deficits is becoming more pressing, as governors and administrators attempt to counter the economic effects of the Covid-19 pandemic.

Central bankers are seeking ways to revive a $4tn market for municipal bonds that allows states and cities to borrow funds for basic infrastructure spending such as schools, hospitals and highways.

On Sunday, New Jersey’s Democratic senator Bob Menendez and senator Bill Cassidy of Louisiana, a Republican, proposed a $500bn fund for state and local governments as part of the next rescue package.

Officials for New York state, which was already facing a multi-billion budget shortfall after losing hundreds of thousands of taxpayers to states with lower taxes, has already warned the state is facing a $10bn hole caused by the pandemic in its $177bn budget.

During his address, De Blasio said he was consulting with counterparts in Miami and Denver on how to handle the approaching financial crisis. But De Blasio’s invocation of an era when crime soared, rodents infested the streets, and entire neighborhoods were considered no-go was also pointed: Trump, raised in Queens, became a classic bridge-and-tunnel entrepreneur, venturing to Manhattan first to play and ultimately to seek a fortune.

“You are failing to protect the very people you grew up around,” the mayor told the president, and warned more broadly: “If cities can’t function, how on earth do you have a national recovery?”

Nearly 14,000 New Yorkers have died since the state’s first coronavirus case was reported on 1 March, according to state data. The state total doesn’t include more than 4,000 New York City deaths that were attributed to the virus on death certificates but weren’t confirmed by a lab test.

New York’s governor, Andrew Cuomo, said states also need money from the federal government to ramp up testing.

“You have the president saying 15 times, ‘It’s up to the governors, it’s up to the governors, it’s up to the governors.’ And then they’re going to pass a piece of legislation that gives you know what to states: zero, zilch, nada, niente,” Cuomo said.

Cuomo said 507 people died from Covid-19 in New York state on Saturday, down 33 from the previous day and by 271 since last Monday. Other indicators were going in the right direction, the governor said. Hospitalizations were down by more than 750, to 16,213.

But Cuomo and De Blasio maintained their warnings that people in New York City and the rest of the state need to stay vigilant to curb the spread of the virus.