I have deleted my last tweet and would like to apologise profusely to anyone who I upset while I was asleep.
The image, which appeared on his online account, followed by 2.8 million people, appeared to have been taken on a plane and showed a piece of paper with offensive words written on it and an arrow pointing towards Clarkson.
It is not clear who took the photograph, which shows his Top Gear sidekick James May in the background.
David Cameron has got behind the wheel of a car for the first time in three years.
But the Prime Minister admitted that his choice of vehicle will not please his friend, the broadcaster and notorious "petrolhead" Jeremy Clarkson, as it was one of the Japanese-made electric cars used to shuttle delegates around the G20 summit in St Petersburg, Russia.
After getting used to being ferried around by chauffeurs in the three years since becoming Prime Minister in 2010, Mr Cameron joked that he was pleased to find that his driving skills remain intact and he did not cause any accidents.
He told reporters in St Petersburg: "I think I will have upset my constituent Jeremy Clarkson by driving an electric car.
"It was the first time I've driven on a road for three years, but there were no accidents, no car crashes."
The BBC has paid Top Gear star Jeremy Clarkson millions of pounds for his share in the company behind the show's international success.
Accounts published today by BBC Worldwide, the corporation's commercial arm, show it paid a total of £16.2 million to take control of the firm called Bedder 6.
The BBC already owned half the firm and the deal saw Clarkson, who had a 30% share, collect more than £8 million while his colleague, Top Gear executive producer Andy Wilman, picked up more than £5 million.
A spokesman for BBC Worldwide said: "No licence fee income was used by BBC Worldwide to pay the exiting shareholders of Bedder 6 in 2012.
"In just five years the business grew its profits five-fold (and its revenue to £149 million), which would not have been possible without the involvement of the show's creative talent."
I have read what Miliband said. And seriously, I'm not sure he's right in the head.
In a speech earlier today, Ed Miliband said:
"Jeremy Clarkson, who may have at least acknowledged the tragedy of people who end their own lives, goes on to call them "Johnny Suicides" whose bodies should be left on train tracks rather than delay journeys.
"It is attitudes like these that reinforce the stigma that blights millions of people's lives, and holds our country back."
The Labour Party has not yet issued a response to Mr Clarkson's tweets.
The Health Secretary Jeremy Hunt said emergency legislation would be hurried through Parliament to deal with the scandal, which he learned about last week.
There is no suggestion that hospitalisation or detention of any patient has been clinically inappropriate, nor that the doctors so approved are anything other than properly qualified to make such recommendations, nor that these doctors might have made incorrect diagnoses or decisions about the treatment patients need.
All the proper clinical processes were gone through when these patients were detained.
We believe no-one is in hospital who shouldn't be, and no patients have suffered because of this.
He said doctors recommending patients to be locked up would not have known they had not been properly approved to make such recommendations.
Health Secretary Jeremy Hunt said there were "irregularities" in the way doctors were approved before they could assess if patients should be detained under the 1983 Mental Health Act.
He told the Commons: "Our latest best estimate is that 2,000 doctors were not properly approved and that they have participated in the detention of between 4,000 and 5,000 current patients within institutions in both the NHS and independent sectors."
Mr Hunt said four of England's Strategic Health Authorities were affected, with some patients sent to Ashworth and Rampton high security hospitals, home to some of the country's most notorious inmates.