President Trump’s pressure campaign on Republican-led states to redraw congressional maps in his party’s favor is testing his power over governors and state legislators at a time when Republicans in Washington have largely rubber-stamped the president’s agenda and acquiesced to his demands.

As Mr. Trump and his political allies stare down the midterm elections — and the prospect of Democrats taking control of the House — they are engaged in a nationwide effort to gobble up as many Democratic-held districts as they can by changing maps typically set once a decade after the census.

The effort is the latest example of Mr. Trump and his allies trying to rewrite the rules to squeeze out every possible political advantage. Throughout his career, Mr. Trump has brushed aside norms, testing the boundaries of executive power and the law. Now, as he tries to secure more G.O.P. seats, he is challenging state leaders to defy him and risk paying the price if they do.

For Mr. Trump, the opportunity to tilt the playing field is not just to gain a political leg up. He sees the current maps as unfair and unrepresentative of his and his party’s political power.

“I won Texas,” Mr. Trump said on Tuesday on CNBC. “I got the highest vote in the history of Texas, as you probably know, and we are entitled to five more seats.”

That argument, however, is wrong — Mr. Trump’s popular-vote win in Texas does not automatically translate to more Republican seats in the state’s congressional delegation.