WASHINGTON, March 24 (Reuters) - U.S. President Donald Trump and New York Governor Andrew Cuomo exchanged verbal shots on Tuesday over the federal response to the coronavirus crisis in the hard-hit state.

Cuomo expressed frustration at his daily news conference that the Federal Emergency Management Agency was sending New York 400 ventilators from a national stockpile when he needed 30,000 to care for the rising list of victims.

"You want a pat on the back for sending 400? We need 30,000," said Cuomo. He added his state would gladly send the ventilators on to other states once the New York crisis passed.

"The rate of new infections is doubling every three days" in New York and threatening to overwhelm hospitals, Cuomo said.

Trump, a long-time resident of New York who recently made Florida his home state, dismissed Cuomo's complaints during a Fox News Channel town hall. The Republican president has said repeatedly that he and the Democratic governor, both from the New York City borough of Queens, have worked well together.

Trump said Cuomo "should have ordered the ventilators" when he had a chance in recent years, and added that the federal government is building temporary hospitals and taking other steps to help New York.

Trump said he was not blaming Cuomo, however.

Cuomo, whose state now stands at ground zero in the U.S. coronavirus outbreak, has been urging the Trump administration to use the Defense Production Act to tell manufacturers they must produce desperately needed supplies for healthcare workers.

Vice President Mike Pence told Fox that the national stockpile has 20,000 and "we have been making those available ... We will continue to prioritize those resources."

(Reporting By Steve Holland Editing by Sonya Hepinstall)

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