Boris Johnson will not make an election pact with Brexit Party leader Nigel Farage, Downing Street has said.
Mr Farage said his party and the Conservatives should make a deal and "together we would be unstoppable".
But a senior Conservative source said Mr Farage was "not a fit and proper person" and "should never be allowed anywhere near government".
Mr Farage said he was "disappointed" with the response as he was offering a "genuine hand of friendship".
He told the BBC's Andrew Neil show that he did not want a job in the Conservative government and accused the Tories of "petty, tribal, party politics".
"Can't we see that actually if we get a Labour government we're not going to get a meaningful Brexit of any kind at all? This is big chance to unite the Leave vote," he said.
"We've got a solution here."
Mr Johnson argues that an election is now the only way to break the deadlock over Brexit, but MPs have twice rejected his call to hold one.
Labour leader Jeremy Corbyn has said he is "eager for an election" but wants to see legislation designed to stop a no-deal Brexit on 31 October implemented first.
Parliament is now prorogued for five weeks and is not scheduled to return until 14 October, when there will be a Queen's Speech outlining Mr Johnson's legislative plans.
Meanwhile, Scotland's highest civil court has ruled that the prime minister's suspension of the UK Parliament was unlawful.
Mr Farage has offered a "non-aggression pact" between his party and the Conservatives, on the condition that Mr Johnson sign up for "a clean-break Brexit" - in other words, no deal.
The aim is try to see off the threat from a "Remain alliance" of opposition parties who oppose Brexit and could depose the Tories.
Mr Farage says he will not field candidates in any of the Conservatives' existing seats and targets if, in return, the Tories stand aside in more than 80 Leave-voting constituencies where they are unlikely to win.
He made the offer in a full-page advert in the Sun and a wraparound advert in the Daily Express on Wednesday.
At the weekend, the Brexit Party leader said the offer was "100% sincere" and would help return Mr Johnson to Downing Street.
He wrote in the Sunday Telegraph: "Johnson should cast his mind back to the European elections in May, in which his party came fifth, and ask himself: does he want the Tories to find themselves in a similarly disastrous position when the results of the next general election come in, or does he want to sign a non-aggression pact with me and return to Downing Street?"
When asked about a potential alliance on the Andrew Marr Show, Chancellor Sajid Javid said: "We don't need an electoral alliance with anyone. We can stand on our own two feet, put our message across."