“Something was building for a while,” Mr. King said. The difficulties of coordinating his Thanksgiving and Christmas travel plans with family amid the unknowns of the impeachment battle, he said, “somehow became like a metaphor” fueling his decision.

The exit of Mr. King, 75, comes as a growing number of Republicans have decided to retire rather than seek re-election as they eye the grim political realities for their party, including an uphill slog to win back the House in next year’s election and the prospect of sharing a ticket with an unpopular president. The dilemma is particularly acute for Republicans in suburban districts, where voters have been alienated by Mr. Trump’s rhetoric and his positions. Mr. King is the 20th House Republican to depart Congress at the end of 2020 because of retirement or seeking another elected office.

Mr. King, who represents parts of Nassau County and Suffolk County as part of New York’s second congressional district, said none of those concerns influenced his decision, pointing to his favorable polling numbers and a sizable war chest. More persuasive, he said, was his daughter’s recent move to North Carolina, and a desire to give New York Republicans plenty of time to find a replacement candidate ahead of primary in April.

“I think it’s gotten too toxic,” Mr. King, a boxer, acknowledged, “but once I’m in the arena, I enjoy the battle.”

He said he called Mr. Trump on Sunday to inform him of his plans, assuring the president that he would use his final months in office to vote against articles of impeachment and support Mr. Trump’s re-election bid, as Republicans seek to prevent any defections in the coming weeks. The president asked him to reconsider retirement, Mr. King said, but ultimately accepted his decision.