Gordon Brown is facing calls to quit on his own website
A call for Prime Minister Gordon Brown to resign has become the best supported petition on the Downing Street website.
The petition - started by Labour supporting academic Kalvis Jansons - has been backed by more than 38,000 people so far.
Petitioners are promised a response from the government if they attract more than 200 signatures.
But Downing Street has not so far commented on whether it will provide a formal response to this petition.
When tackled about it earlier this week, the prime minister's official spokesman said Mr Brown was "focusing on addressing the needs of the people of the UK and in particular focusing on the big economic issues that we faced in response to the global economic downturn that we were having to deal with".
A Downing Street spokesman denied there was any embarrassment at Number 10 over the petition, saying there had been similar calls in the past and there was "never any attempt to censor material which is critical of the prime minister or the government".
Mr Jansons, Emeritus Reader in Mathematics at UCL, in London, has described himself as a "traditional Labour supporter" who has become disillusioned with New Labour.
He told The Guardian the "final straw" was Mr Brown's initial reluctance to apologise for e-mails by his former special adviser Damian McBride smearing senior Conservatives.
In the petition's introduction, he says: "There are many reasons why we might want Brown to resign, but rather than having lots of narrow petitions on this topic (most of which have been rejected), I wanted one for all of us."
The deadline to sign the petition is 22 October.
The next most popular petition is a campaign to protect the RNLI from paying licence fees for using maritime radio frequencies, which has 28,555 signatures.
That is followed closely by a call to make savings account providers publish the current interest rates on their statements and a petition no to reduce the national speed limit to 50mph.
The Downing Street petition site has attracted controversy since it was launched in November 2006, with an unnamed government minister describing its creator as a "prat".
The most well-supported petition to date was a campaign against road charging, signed by nearly two million people.
A petition calling for Top Gear presenter Jeremy Clarkson to be the prime minister was signed by 50,000 people prompting a video response from Number 10, in which it said they had "thought long and hard" about the suggestion but "on second thoughts...maybe not".