WASHINGTON—Elon Musk’s tenure working for the Trump administration is coming to an end, just as the billionaire DOGE czar is using his perch to put more pressure on Republicans to shrink the size of government.

In a message on his X social-media platform late Wednesday, Musk said he was moving on and thanked President Trump for the “opportunity to reduce wasteful spending.” He predicted his cost-cutting drive will become a “way of life throughout the government.”