Trump, a Republican who has offered frequent commentary on the New York mayoral election, injected himself further into the race by crossing party lines to support Cuomo over Mamdani and the Republican candidate, Curtis Sliwa, who trails badly in public opinion polls in the heavily Democratic city.
Cuomo is running as an independent after losing to Mamdani in the Democratic primary.
Tuesday's New York City election has been closely watched nationally as one that could help shape the image of the Democratic Party as it seeks its identity in opposition to Trump.
Mamdani, 34, a self-described democratic socialist who leads Cuomo in the polls, has energised younger and more progressive voters, but he has alarmed more moderate Democrats who fear a shift too far to the left might backfire.
Republicans have attacked Mamdani's candidacy throughout the campaign, with Trump casting him as a communist.
"Whether you personally like Andrew Cuomo or not, you really have no choice. You must vote for him, and hope he does a fantastic job. He is capable of it, Mamdani is not!" Trump wrote on his Truth Social platform.
"If Communist Candidate Zohran Mamdani wins the Election for Mayor of New York City, it is highly unlikely that I will be contributing Federal Funds, other than the very minimum as required, to my beloved first home," said Trump, a native New Yorker.
The US federal government is providing $US7.4 billion ($A11.3 billion) to New York City in fiscal year 2026, or about 6.4 per cent of the city's total spending, according to a report from the New York State Comptroller.
Trump has threatened federal funding cuts throughout his second term in office over climate initiatives, transgender policies, pro-Palestinian protests against Israel's war in Gaza and diversity, equity and inclusion practices.
Mamdani, a Uganda-born state assembly member, shocked political observers on June 24 with a convincing victory in the primary.
Mamdani has used his campaign to rally New Yorkers against establishment candidates such as Cuomo, who was elected governor of New York three times but resigned in 2021 following a report from the New York attorney-general that concluded he had sexually harassed 11 women, including state employees.
A US Justice Department investigation later concluded Cuomo subjected at least 13 female state employees to a "sexually hostile work environment".
"The MAGA movement's embrace of Andrew Cuomo is reflective of Donald Trump's understanding that this would be the best mayor for him," Mamdani said at a campaign event.
"(Trump and Cuomo) share the same donors, they share the same small vision, they share the same sense of impunity."
Mamdani's policies include hiking taxes on New York City's wealthiest, raising the corporation tax rate, freezing stabilised apartment rental rates and increasing publicly subsidised housing.
