In the interview on Thursday, she also faulted what she called the governor’s “transactional” approach to government, which, she said, was designed to get “good headlines,” but has “not changed the dynamic of the upstate economy.”

Ms. Miner’s decision came as a disappointment for Democrats who were hoping she would challenge Rep. John Katko, a Republican who represents the district that includes Syracuse, where she was mayor for eight years until term limits forced her to step down on Dec. 31.

The district has swung between Republicans and Democrats, and some observers believed that Mr. Katko might be vulnerable since he voted for President Trump’s tax plan, which hurts high-tax states like New York by capping the deductibility of state and local taxes.

Geoff Berman, executive director of the New York State Democratic Party, said the loss of Ms. Miner’s candidacy against Mr. Katko was a blow to the party’s efforts to make inroads into the Republican-controlled Congress. “It’s unfortunate that Stephanie chose not to capitalize on her local name ID and help the party take on Washington Republicans,” Mr. Berman said.

When asked of Ms. Miner’s consideration of a primary challenge to Mr. Cuomo, Mr. Berman deflected, saying the governor’s progressive agenda “sets a solid foundation for a third term.”

Bill Mulrow, chairman of Mr. Cuomo’s re-election campaign, also defended the governor’s progressive record, pointing to measures like a $15 minimum wage, paid family leave, gun control, a ban on fracking and free college tuition at public colleges for the middle class.

“Gov. Cuomo has the strongest progressive record of any elected official in this country — period,” he said. “And we look forward to building on that record in the third term.”