Democratic state legislators from Texas who fled their state Sunday to try to block the passage of gerrymandered U.S. House maps stood on Monday with Gov. Kathy Hochul of New York with a message: Any notion of fair political mapmaking has ended.

“If Republicans are willing to rewrite these rules to give themselves an advantage, then they’re leaving us no choice; we must do the same,” Ms. Hochul told reporters in Albany.

Flanked by Assembly Speaker Carl E. Heastie in the ornate Red Room of the State Capitol, Ms. Hochul vowed to pursue every avenue to maximize Democrats’ electoral chances, including amending the State Constitution to kill New York’s independent redistricting commission.

“I’m tired of fighting this fight with my hand tied behind my back,” Ms. Hochul said. “With all due respect to the good government groups, politics is a political process.”

The Democrats’ position was something of a Texas Two Step. Lawmakers are trying to thwart Republican efforts to redraw the House maps in Texas, even as they reserve the right to do it in New York and other states that they control. Ms. Hochul’s comments were the clearest indication yet that Democrats in her state aim to throw out the rulebook in their efforts to counter President Trump.

At the president’s request, Republican leaders in Texas unveiled a new map last week that would redraw five Democratic seats to include many more Republican voters. Democratic members of the Texas House then fled the state to deny the Republican majority the quorum the State Constitution requires for legislation to pass — temporarily at least.