Mr. Cuomo, a former federal housing secretary and state attorney general, has spent a good deal of his re-election campaign attacking the Republican president and his policies, particularly since he won a wide victory in a Democratic primary over actor Cynthia Nixon.

This focus—in speeches and advertisements—has led Mr. Cuomo’s rivals to accuse him of lacking vision for the office. On Thursday, they spent an hour debating ideas on charter schools, protecting transgender rights and improving the upstate economy during a League of Women Voters forum in Albany. The governor, leading in the polls, declined to attend and instead held a telephone rally with Long Islanders that was closed to the press.

“The governor will be spending the final days of the campaign speaking directly with voters and helping to elect Democrats up and down the ticket,” said Lis Smith, a spokeswoman for Mr. Cuomo.

The governor spent the week before the election at government events, including two to review taxpayer-funded airport upgrades in Rochester and Syracuse. Rebuilding the state’s infrastructure—from New York City’s subways to new highway rest stops in the Adirondacks—has been a focus for Mr. Cuomo, and one his advisers say will continue in a third term.

“A lot of it will be expanding a lot of what he’s already done,” said Bill Mulrow, the chair of Mr. Cuomo’s re-election effort and his top governmental aide from 2015 to 2017. “Obviously he’s focused on not having New York go backwards, and that’s part of the reason he’s been fighting back against Trump and Washington, to protect the progress we’ve already made in New York.”

Mr. Cuomo has been campaigning to help Democrats win a majority in the 63-seat state Senate, which is controlled by 31 Republicans in alliance with a renegade Democrat from Brooklyn. At rallies with Democratic candidates, Mr. Cuomo has pledged quick legislative pushes on a bill to recodify abortion protections as well as a “red flag” bill that would allow family members and teachers to petition a court to have firearms taken from someone they believe could harm themselves or others. State Senate Republicans haven’t allowed votes on either measure.

The governor says he will work with Senate Democrats to push for voting reform, and will push congestion pricing to create a funding stream for the Metropolitan Transportation Authority. Declines in the reliability of New York City’s subways have frustrated riders and were a point of attack on the governor, particularly from Ms. Nixon. An MTA plan to upgrade and modernize the system would cost $40 billion over 10 years.

Mr. Mulrow also said the governor wasn’t embracing a single-payer health-care system for the state or calls from progressive groups to increase taxes.

At the forum, other gubernatorial candidates criticized Mr. Cuomo for mismanaging economic development efforts—two former advisers were convicted of federal corruption charges this year, though the governor has never been accused of wrongdoing— and for chasing political glory over governmental substance.

“Are we going to give Cuomo a free ride, or are we going to demand more?” Green Party candidate Howie Hawkins asked.

A supporter of his campaign attended the debate in a chicken suit, wearing a Cuomo sign.