“I don’t like criticizing people,” Mr. Bush said in an interview Thursday with The Wall Street Journal aboard his campaign bus in New Hampshire. “But I do think that Marco, and any other United States senator and any other congressman, needs to show up, and so, Marco’s fair game.”

Mr. Bush’s debate scolding of Mr. Rubio’s Senate absenteeism backfired when the senator cast the attack as petty politics. Mr. Bush and his allies, however, haven’t stopped talking about it.

A super PAC backing the former governor took Mr. Rubio to task on Twitter Thursday afternoon for missing a Senate Intelligence Committee hearing about the possibility of a bomb downing a Russian airliner over Egypt. “He’ll go through the wringer, just like I’m going through it, and he’ll have to defend himself,” Mr. Bush said. “There’ll be scrutiny on him, just as there should be for everybody.”