In the Oval Office on Friday, President Donald Trump defended Carr and said "I disagree with Ted Cruz", who is ordinarily one of his staunchest allies.
Another Republican Senator, Thom Tillis of North Carolina, told reporters that Cruz was "absolutely right" in his criticism of Carr.
Tillis, who will not seek re-election next year, said the FCC chairman's comments were "just unacceptable behaviour".
Republicans in Congress have generally been toeing the party line with their response to Kimmel's suspension as the nation is shaken by the political and cultural aftershocks of Kirk's killing.
But Senator Jerry Moran, a Republican from Kansas, sounded a note of caution on Thursday.
"The conservative position is free speech is free speech, and we better be very careful about any lines we cross in diminishing free speech," Moran told Politico.
South Dakota Senator Mike Rounds said he would approach it as an "employer-employee issue".
Kimmel has not publicly commented about his suspension, but his late-night colleagues - including Jon Stewart, Jimmy Fallon and Stephen Colbert - responded on Thursday with a show of solidarity.
Kirk was fatally shot on 10 September during an open-air event on a Utah college campus.
On Thursday, the Senate passed a resolution to designate 14 October - Kirk's birthday - a day of remembrance for him.
Lawmakers in the US House of Representatives approved the resolution, but nearly 100 Democrats opposed it.
In Sacramento, California, police said three shots were fired on Friday afternoon into a window of an ABC10 building while people were inside.
The shots came from a moving vehicle and nobody was injured, police said.
It was not immediately clear if the shooting was a targeted attack or an accidental discharge of a weapon.
ABC10 is an affiliate operated by Nexstar, one of the major media companies that cancelled Jimmy Kimmel Live! from its markets this week, citing the host's "offensive and insensitive" comments about Kirk.