The network, which helped make Mr. Trump a force on the American right, devoted little airtime to his speech. It did not broadcast his remarks live — and hasn’t done so for most of his rallies over the past year.

But it did go live with a competing speech that former Vice President Mike Pence delivered the same day, at a hotel less than a mile away. For roughly 17 minutes on Tuesday afternoon, Fox viewers heard Mr. Pence uninterrupted.

The snub reflected a pattern in the way that Fox’s news programming has treated the former president lately: skeptically and sometimes harshly, even as the network’s highly rated and influential prime-time hosts, like Sean Hannity, continue to defend him and deflect from the recent revelations of the Jan. 6 hearings.

Fox sent a reporter to cover Mr. Trump on Tuesday and included snippets of his speech in its coverage throughout the day. But the network’s practice since Mr. Trump left office has been to largely ignore his frequent political rallies, leaving them to smaller, more devoted outlets like Newsmax and One America News, which carry them live and often in full.