The row started after Kimmel said in his monologue on 15 September that the "Maga gang" were "desperately trying to characterise this kid who murdered Charlie Kirk as anything other than one of them" and trying to "score political points from it".
He also made fun of Trump's reaction to the influencer's murder, showing a clip of the president responding to a question about how he was mourning the death by changing the subject to construction of a new White House ballroom.
Kimmel compared the response to "how a four-year-old mourns a goldfish".
Brendan Carr, the Trump-appointed chair of broadcast regulator the Federal Communications Commission (FCC), threatened to act against ABC and its parent company Disney over Kimmel's remarks.
The spat comes as Vice President JD Vance and other White House allies have been pushing a national campaign to punish anyone who has criticised Kirk in the wake of his death.
Hours after Mr Carr made his initial remarks about Kimmel's monologue, Nexstar said it would not air Kimmel's show "for the foreseeable future".
Sinclair followed suit and ABC announced that it would "indefinitely" suspend the programme and demanded an apology from Kimmel, as well as a donation to Kirk's non-profit organization Turning Point USA.
Mr Carr thanked Nexstar "for doing the right thing" and said he hoped other broadcasters would follow its lead. Nexstar is currently seeking FCC approval for its planned $6.2bn (£4.5bn) merger with Tegna.
Anna Gomez, the sole Democrat on the FCC, said on Monday that she was "glad to see Disney find its courage in the face of clear government intimidation".