Governor Andrew Cuomo met the president on Thursday to discuss the Trump administration’s decision to block New Yorkers from programmes which allow travellers to avoid long security lines at the US border.
The administration has sparred with the Democratic governor over New York’s new “Green Light” law, which lets unauthorised immigrants obtain state driver's licenses and bars federal immigration agents from accessing state motor vehicle records.
On Thursday, the president linked the block on the programme to a number of lawsuits filed by New York’s attorney general, Letitia James, against his administration and his businesses.
“He [Governor Cuomo] must understand that National Security far exceeds politics,” Mr Trump wrote on his Twitter account.
He added: “New York must stop all of its unnecessary lawsuits & harassment, start cleaning itself up, and lowering taxes.”
The Trump administration has claimed it blocked New Yorkers from enrolling in Global Entry and other “trusted traveller” programmes because the cut-off from state records threatened public safety.
New York has sued the Trump administration in response to its expulsion.
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Mr Trump’s linking of his administration’s policies against New York and the state’s lawsuits against him has been described as “corrupt” by a number of high-profile Democratic politicians.
“Trump abused his power to coerce Ukraine into announcing investigations for his personal benefit by freezing military aid,” Adam Schiff, the Democratic chairman of the House Intelligence Committee, said.
“Now, he's using his powers to coerce states to stop investigations into him and his businesses.”
Meanwhile, Walter Shaub, a former director of the US Office of Government Ethics in the Obama administration, repeatedly accused Mr Trump of attempting “quid pro quo extortion” on his Twitter account.
The president was recently acquitted of a so-called quid pro quo with Ukraine over allegations that he withheld millions of dollars in military aid from Ukraine to force an investigation into his Democratic presidential rival Joe Biden.
After Mr Trump and Governor Cuomo’s meeting on Thursday, a statement from Chad Wolf, the acting Department of Homeland Security chief, said the discussion had been productive and talks would continue.
“We will continue discussions with the State of New York to find a mutually agreeable solution,” Mr Wolf said.
In response to Mr Trump’s tweet, Ms James reminded the president that she is responsible for lawsuits in the state, not the governor.
“When you stop violating the rights and liberties of all New Yorkers, we will stand down,” the New York attorney general said.
“Until then, we have a duty and responsibility to defend the Constitution and the rule of law.
"BTW, I file the lawsuits, not the Governor."
Mr Trump has had a fraught relationship with New York in recent years and has accused officials of harassing his businesses in search of “anything at all they can find to make me look as bad as possible.”
The president also said last year that Florida would become his permanent residence after he leaves the White House instead of New York, which has long been his home.
He claimed he had been “treated very by the political leaders of both the city and state.”
Mr Cuomo replied: “Good riddance. It’s not like Donald Trump paid taxes here anyway.
“He’s all yours, Florida.”
In September, Manhattan district attorney’s office sent Mr Trump’s accounting firm a subpoena for eight years of tax returns.
The president has denied wrongdoing and said he pays “millions of taxes”.
Additional reporting by AP