Baker, a moderate Republican in a deep-blue state, faced a Trump-backed primary challenge and a potentially difficult general election.

Charlie Baker of Massachusetts, a moderate Republican who defied former President Donald J.

Baker and his lieutenant governor, Karyn Polito, wrote in a letter to supporters.

Baker, 65, who is more popular in polling among Democrats and independent voters than he is among fellow Republicans, confronted a Trump-backed primary challenge and a general election in which he could have faced the state’s popular attorney general, Maura Healey, a Democrat.

Baker is a popular, even-keeled, nonideological New England Republican who has been a proponent of abortion rights, same-sex marriage and some gun control measures.

Baker, along with Govs.

Baker avoided commenting on Mr.

Healey, of the establishment’s center left, against the progressives Sonia Chang-Díaz, a state senator, and Ben Downing, a former state senator.

Baker faced a difficult Republican primary challenge from Geoff Diehl, a former state representative who was chairman of Mr.

Baker to retain the Massachusetts governor’s office for Republicans.