Churkin died one day before his 65th birthday. He was known as a deeply intelligent, combative, disarming and humorous fixture at the UN Security Council.
The diplomat suffered from cardiac arrest while at the Russian Mission on East 67th Street, a law enforcement official said. He was taken to New York-Presbyterian Hospital, where he died.
Preliminary information suggests there was no foul play in Churkin's death, New York police Lt. Thomas Antonetti said. But authorities are waiting for reports from the New York City medical examiner's office before releasing the official cause of death.
The Russian Foreign Ministry said, "The outstanding Russian diplomat died while he was in his current working role." And President Vladimir Putin "expressed sympathy to the friends and family as well as to the staff of the Russian Foreign Ministry," the Kremlin said.
Members of the UN General Assembly stood for a moment of silence in memory of their colleague.
"We've lost one of the most respected and influential members of the UN family," UN General Assembly President Peter Thomson said. "I can say with confidence that his name's going to live on in the annals of this organization's history."
Thomson said Churkin will be remembered for "his great intellect and his consummate diplomatic skills, and for his good humor and consideration for others."
Thomson added: "Not only has Russia lost one of its truest sons, but here at the United Nations, we've lost one of our truest."
At the end of the moment of silence, Thomson said: "Rest in peace, dear Vitaly."
A gracious, formidable colleague
UN Secretary-General Antonio Guterres said, "Ambassador Churkin was a uniquely skilled diplomat, a powerful orator with great wit, and a man of many talents and interests."
Members of the Security Council said they were "deeply saddened" to learn of Churkin's death. Churkin spent more than 40 years at the Russian Diplomatic Service and headed the Russian Mission to the United Nations for more than a decade, the Security Council said.
He was often at odds with the United States, the United Kingdom and France. China would often take its cue from how Russia would vote.
For a decade, it was Churkin who raised his arm to veto numerous resolutions ranging from the Syrian crisis
to the Malaysia Airlines crash over eastern Ukraine
He stood firm in supporting Syrian President Bashar al-Assad's regime against Western attacks. And he cited US policy in Libya as a symbol of failure by Western countries who favored regime change.
Nikki Haley, US ambassador to the United Nations, called Churkin "a gracious colleague."
"We did not always see things the same way, but he unquestionably advocated his country's positions with great skill," she said in a statement.
Susan Rice, a former US envoy to the United Nations, said Churkin was "a formidable adversary, but always a friend."
Another former US ambassador, Samantha Power, said she was heartbroken by Churkin's death and credited him with trying to help improve Russian-US relations.
"Devastated by passing of UN ambassador Vitaly Churkin," Power tweeted. "Diplomatic maestro & deeply caring man who did all he (could) to bridge US-RUS differences."
And Gérard Araud, a former French ambassador to the United Nations, said Churkin was an "extraordinary colleague" during Araud's five years on the Security Council.
"Abrasive, funny and technically impeccable," Araud tweeted about Churkin
. "Sincere condolences."