Ukip and the Greens could take part in a televised leaders' debate ahead of next year's general election, David Cameron has suggested.
Mr Cameron indicated that he is interested in staging a variety of debates, which could include one featuring all the party leaders and another which would pit him against Labour's Ed Miliband as the two men who could become Prime Minister.
But Ukip leader Nigel Farage said he still expects the Prime Minister to dodge a debate with him, predicting that Conservatives will find a reason for opting out once discussions get under way between the parties and broadcasters in the autumn.
Mr Cameron's comments appeared to confirm reports last weekend that Downing Street envisages a "5-3-2" format for three debates to be held before and during the election campaign - one featuring the leaders of the Conservatives, Labour, Liberal Democrats, Ukip and Greens, one with Mr Cameron, Mr Miliband and Deputy Prime Minister Nick Clegg and one head-to-head between the leaders of the two biggest parties.
The Prime Minister told BBC Breakfast: "I have suggested perhaps we should have one debate with all of the parties and so everyone can have their say, and perhaps we need a debate where the two people who could be Prime Minister debate directly with each other.
"You can have a debate where you have all of the parties. I don't think we could have a party like Ukip without an MP if you don't have a party like the Greens, who have an MP."
Mr Cameron also repeated his proposal that some of the debates should take place before the election campaign formally gets under way.
"I'm keen to have debates before the next election," he said. "Now we have got a fixed-term parliament, we don't need all these debates in the general election. Last time they rather took the rest of the life out of the general election. I actually like getting out into the schools and hospitals and public meetings and workplaces, talking to people not just taking part in debates, so let's start before the elections. I'm very keen to examine all the different formats we can have."
He added: "There are still a number of issues that have to be ironed out. But I helped make the debates happen last time. I am pro-TV debates.
"We have to find the right format but I am sure, if our teams sit down, they can come up with the right formula."
But Mr Farage - who recently took on Mr Clegg in a pair of televised debates on Europe - accused Mr Cameron of planning to dodge a showdown with him.
The Ukip leader told LBC 97.3 radio: "They are thinking about it and they won't say anything until after the party conference season in October and then they will decide it's not a very good idea.
"He doesn't want to have a debate with me. Of course he doesn't, because he knows that there are two issues on which he can't win. One is the European question - the promise of a referendum. Five years ago, this bloke won the European elections giving us a cast-iron guarantee that if he ever became Prime Minister there would be a referendum on the Lisbon Treaty, and he let us down.
"But the big one and the one that no-one wants to debate, and the reason they are throwing all this abuse at us, is this - it is completely pointless to talk about immigration figures and targets while we are members of the EU and we have a total open door to nearly half a billion people and we cannot control the numbers that come."
In a later interview with BBC Radio Suffolk, Mr Cameron insisted he was not trying to dodge a debate with Farage
"Absolutely not," he said. "The TV debates happened at the last election really because I was very keen to get them under way.
"I'm keen for them to continue, so I'm not dodging anybody."
Mr Cameron acknowledged that Mr Farage's message was "attractive" to voters, but said Ukip would not be able to deliver on it.
He added: "I think that what people can see with Ukip is that they are saying a lot of things that people find attractive - or at least the leadership of the party are saying some attractive things. Some of their candidates are saying some quite appalling things, and it does raise a question of their competence that they have in their party people who make so many extraordinary statements.
"The real issue in this election is not what people say but what people can do. The fact is there is only one party, one Prime Minister, that can deliver the in/out referendum that we need, and that's me.
"Farage and Ukip can say these things but they can't actually deliver them."
The Prime Minister acknowledged that voters were "frustrated" about the pace of economic growth, immigration and welfare reform, but urged them not to cast a protest vote.
In a message to voters, he said: "Remember, when you vote, you are sending people to run your local council, set your local council tax, you are sending people to the European Parliament who will legislate on the regulations faced by British business and the bills paid by the British taxpayers.
"We need the politics of the answer. We need parties who have a plan, as we have a plan in the Conservative Party, to deal with these things.
"Just sending a message or making a protest doesn't actually, I think, achieve what people want."
Asked if he regarded Ukip as a racist party, Mr Cameron said: "During this election we have seen some extraordinary statements - in many cases very, very unpleasant statements - by Ukip financial backers and candidates, and I think it does go to the issue of the competence of the party.
"What on Earth are they doing selecting people and allowing people like this to be in their party?"
Mr Farage acknowledged that there were "a few idiots" in his party but insisted it was not racist. He argued that media coverage of their comments reflected an effort by the establishment to counter the party's challenge to the status quo.
He told LBC: "This is the political class clubbing together, using their mates in the media and doing anything they can to stop the Ukip charge... It's because we are challenging the establishment and this is what the establishment does."
Mr Farage added: "Because we've got a few idiots in our party - as by the way does every other party - somebody in some part of England says something stupid or offensive on Twitter at midnight, and this is held up as being representative of the view of the party."
A senior Lib Dem source said: "Both the Liberal Democrats and Labour have repeatedly said that we are ready to sign up to TV debates on the same format as last time.
"It is David Cameron and the Conservative Party that have been ducking and weaving and looking for excuses not to do them.
"If the Tories are serious about TV debates, they should stop dragging their feet and get round the negotiating table."
Labour shadow cabinet office minister Michael Dugher said: "This is yet another desperate attempt to dodge talks about TV debates - David Cameron has stalled at every opportunity so far.
"If he is serious about this, he should stop dithering, appoint his negotiators and get on with it.
"It's nonsensical for Cameron to say he wants to start the debates early, but the negotiations late.
"Labour wants talks with broadcasters to start immediately, but Cameron clearly doesn't. Instead of continuing to duck and dive, finding fresh excuses to squirm his way out of the negotiations, he should just get on with it. What is he so scared of?"