On Thursday afternoon, Gov. Kathy Hochul of New York found herself in a situation she had hoped would never come to pass: on the phone congratulating Donald J. Trump, the Republican president-elect.

Ms. Hochul, the leader of the nation’s second largest Democratic state, was an outspoken surrogate for Vice President Kamala Harris during the presidential campaign. She spent months warning that Mr. Trump’s return to power posed an existential threat to what New York values, from abortion rights to immigration.

But confronted with his sweeping victory this week, including surprising gains in deep blue pockets of New York, Ms. Hochul appears more inclined toward cooperation than combat — at least for now.

In sober remarks after the election results became clear, the governor stressed that New York was once again prepared to fight if Washington targets the state’s liberal abortion, gun and climate laws. Far from declaring herself part of the resistance, though, Ms. Hochul said she was ready to work with “him or anybody regardless of party.”

She said she delivered a similar message directly to Mr. Trump in a private call, stressing her opposition to curtailing abortion access but also the possibilities for collaboration around revitalizing Penn Station, the subways and the state’s budding semiconducting industry.

Both sides described the conversation as cordial.

It was a sharp tone shift away from that of other prominent Democratic governors. Gov. Gavin Newsom of California quickly stepped back into the role of opposition leader, announcing a special legislative session “to safeguard California values and fundamental rights.” In Illinois, Gov. J.B. Pritzker mocked Mr. Trump’s competence and vowed to be “a warrior” for Democratic values. “You come for my people, you come through me,” he said.