Clarkson was suspended for allegedly hitting a producer,
the BBC reported last week, and "Top Gear" -- a highly popular show with a big global audience -- was not broadcast as scheduled Sunday.
The BBC's decision to take the show off the air pending an investigation has outraged many of Clarkson's die-hard fans.
More than 990,000 of them have signed the petition posted on Change.org
by Guido Fawkes, a right-wing political blogger, just a week ago. Whether the show of support will have any impact on the BBC's response is unclear.
Clarkson tweeted his thanks Friday night to those who are calling for his reinstatement, saying he is "very touched."
The findings of the internal investigation are due to be presented to the corporation's director general next week, the BBC said Thursday. "Once this has been considered, we will set out any further steps," a statement said.
The BBC said in an earlier statement
that Clarkson, one of the corporation's highest earners, had "a fracas with a BBC producer."
In an indication of its popularity, "Top Gear" was named as the world's most widely watched factual program in the Guinness World Records
2013 Edition book, with an estimated 350 million global viewers.
The show is sold to 214 territories worldwide.
Clarkson vents fury
Clarkson vented his apparent frustration in an expletive-filled speech Thursday night in what seemed to be a spontaneous appearance at a charity auction in north London.
A CNN reporter who was at the event heard Clarkson swear liberally as he talked about his suspension from the show, saying the BBC "have f***** themselves" and that it had ruined a great show.
Clarkson also auctioned what he said would be one final lap of the "Top Gear" track in Surrey, outside London -- used in the show for putting vehicles through their paces -- for £100,000 ($148,000.) It's not clear whether he had the authority to offer the use of the track for auction -- but his words seem to suggest he doesn't expect his BBC career to continue, even if no decision is expected before next week.
"I didn't foresee my sacking, but I would like to do one last lap," Clarkson said. "So I'll go down to Surrey, and I'll do one last lap of that track before the f****** b******* sack me."
Whoever placed the winning bid would be able to ride in a car with him on that lap, he said, or in a rare LaFerrari supercar owned by a friend.
Clarkson, who's been presenting the show since the late 1980s, added, "I'll be a bit tearful when I do it."
The controversial star has at least one influential ally
-- UK Prime Minister David Cameron.
"I don't know exactly what happened," Cameron told the BBC last week.
"He's a constituent of mine, a friend of mine. He's a huge talent.
"Because he is such a huge talent and he amuses and entertains so many people, including my children, who'd be heartbroken if 'Top Gear' was taken off air, I hope this can be sorted out, because it's a great program and he's a great talent."
It is not the first time that Clarkson has been at the center of controversy.
Last May, the television star asked for forgiveness
after using a racist term during a taping of the show.
Clarkson had mumbled the N-word while reciting a children's nursery rhyme, but that version of the take was never aired.
Last year, the BBC show hit the headlines when Argentina complained
about a "Top Gear" special filmed in the country in which the number plate H982 FKL was used -- interpreted by some as a reference to the 1982 Falklands War.
In a previous article on its website, the BBC said
"Jeremy Clarkson is not a man given to considered opinion."