President Donald Trump believes that former New York State Gov. Andrew Cuomo has a solid chance of defeating Democratic Party nominee Zohran Mamdani in New York City's election for mayor."I would think that he would have a good shot at winning," the president told reporters at the White House on Tuesday, as he referred to Cuomo.Trump offered his political punditry the day after Cuomo announced that he would continue his mayoral bid as an independent candidate.The former three-term governor, who is gunning for a political comeback after resigning in 2021 amid multiple scandals, was convincingly defeated last month by Mamdani in the Democratic Party's mayoral primary.RNC CHAIR CLAIMS MAMDANI FACE OF THE NEW DEMOCRATIC PARTYMamdani's primary victory over Cuomo and nine other candidates rocked the Democratic Party, and boosted the Ugandan-born 33-year-old state assemblyman from Queens toward becoming the first Muslim and first millennial mayor of the nation's most populous city.Trump said that Cuomo's "got to run a tough campaign."Mamdani, who was backed by progressive champions Rep. Alexandria Ocasio-Cortez of New York and Sen. Bernie Sanders of Vermont, surged to a primary victory over then-frontrunner Cuomo thanks to an energetic campaign that put a major focus on affordability and New York City's high cost of living.TRUMP ARGUES NYC FACES DIRE CONSEQUENCES IF COMMUNIST MAMDANI BECOMES MAYORMamdani made smart use of social media platforms, including TikTok, as he engaged low-propensity voters. He proposed eliminating fares to ride New York City's vast bus system, making CUNY (City University of New York) "tuition-free," freezing rents on municipal housing, offering "free childcare" for children up to age 5, and setting up government-run grocery stores.Trump, in his comments Tuesday, repeated his claim that Mamdani is a "communist.""I dont think that race is over yet. We do have a couple of people running. There are things coming out about him," Trump added, as he referred to Mamdani.Republicans have spotlighted recent news items regarding Mamdani that have gone viral. They include a 2020 photo Mamdani posted online that shows him flipping off a statue of Christopher Columbus, stories about comments Mamdani made last December when he said as mayor he would arrest Israeli Prime Minister Benjamin Netanyahu and his recent comments in a cable news interview that "I have many critiques of capitalism."'IN IT TO WIN IT': CUOMO REFUSES TO BACK DOWN IN HEATED NYC MAYORAL RACE AGAINST ZOHRAN MAMDANICuomo, during the final days of the primary campaign, shined a spotlight on unrest last month in Los Angeles to raise warnings about Trump, and showcase his own experience. And Cuomo pledged, if elected mayor, to mount a national campaign to try and thwart Trump's agenda, vowing to protect New York City from what he suggested could be a possible future federal crackdown against immigration protests in the city.But Mamdani campaign spokesperson Jeffrey Lerner, highlighting Trump's comments, said on Tuesday that "we would like to congratulate Andrew Cuomo on earning Donald Trumps endorsement. Obviously, this triumph speaks for itself. The question now is whether Cuomo will embrace Trumps support publicly or continue to just accept it in private."Trump's apparent vote of confidence in Cuomo comes despite Mayor Eric Adams also being on the general election ballot. The embattled mayor announced earlier this year that he would seek re-election as an independent candidate.ANDREW CUOMO OPENS UP ON WHY HE LOST THE MAYORAL PRIMARY TO MAMDANIAdams' poll numbers were sinking even before he was indicted last year on five counts, which accused the mayor of bribery and fraud as part of an alleged "long-running" scheme to personally profit from contacts with foreign officials.The mayor made repeated overtures to Trump, and the Justice Department earlier this year dismissed the corruption charges so Adams could potentially work with the Trump administration on its illegal immigration crackdown.Cuomo, in a video on Monday announcing his decision to stay in the race, said, "Only 13% of New Yorkers voted in the June primary. The general election is in November, and I am in it to win it."And Cuomo charged, "My opponent, Mr. Mamdani offers slick slogans but no real solutions."While he acknowledged Mamdani's victory in the primary, Cuomo left the door open to a November run as an independent candidate, which election rules in New York state permit.And late last month, Cuomo let pass a deadline for candidates who had already qualified to run as independents to decline that independent ballot line.But sources told Fox News at the time that Cuomo had not committed yet to running an active general election campaign through the summer and into the autumn.While polling in recent days suggests Mamdani is not running away with the race, Cuomo faces an uphill climb in the general election. In deep blue New York City, the Democratic primary winner is largely favored to win the general election. And some of the unions and elected officials that supported Cuomo in the primary are now backing Mamdani.Also on the ballot in the general election are Jim Walden, a former federal prosecutor running as an independent, and Guardian Angels co-founder Curtis Sliwa, who for a second straight election is the Republican mayoral nominee.Walden has proposed that an independent survey be conducted in September to determine which candidate would have the best shot of defeating Mamdani, with the other candidates agreeing to drop out.But having Cuomo and Adams agreeing to such a scenario seems remote, as both have urged the other to exit the race.Fox News' Courtney De George contributed to this report.