UK opposition leader David Cameron on why he does not want President Blair
Downing Street has denied reports that Gordon Brown is helping lobby for Tony Blair to become European president.
The ex-PM has not confirmed he wants the job, which will only exist when the EU Treaty is ratified by all 27 states.
Mr Brown's spokesman said officials had "not been asked to go and lobby for Tony Blair's candidacy".
Tory leader David Cameron opposes the treaty and the new post, but said: "We don't support Tony Blair in that role even if there is a president."
The Czech Republic is the only EU state which has not yet signed up to the treaty.
Its constitutional court has been considering whether the treaty is legal under Czech law and is likely to make a ruling on 3 November. If it says it is, the pressure on President Vaclav Klaus to ratify the treaty will increase.
The Guardian says the prime minister's Europe adviser, John Cunliffe, and the UK's EU ambassador, Kim Darroch, have been asked to take soundings on a Blair presidency.
Mr Brown's spokesman said: "There wouldn't be any sense in the prime minister doing that, given we haven't got a treaty ratified and Tony Blair has not indicated whether or not he wishes to be a candidate.
"If the treaty is ratified and if Tony Blair wishes to be a candidate for the role, the prime minister has clearly said he will have his full support."
Until then, the matter remained "hypothetical", the spokesman said.
EUROPEAN COUNCIL PRESIDENT
Scope of role not yet strictly defined
Serves for two-and-a-half years, can be renewed once
Elected by qualified majority by European Council
Chairs European Council
Represents EU internationally on common foreign, security policy
There is some pressure on Mr Blair to confirm he is in the running for the newly created post of president of the European Council, amid opposition to his candidacy among some smaller European states.
Belgium, the Netherlands and Luxembourg are reportedly among smaller countries that believe the president should come from a country that uses the euro and is part of the border-free Schengen Agreement.
Italian Prime Minister Silvio Berlusconi has backed Mr Blair, but there are reports French President Nicolas Sarkozy is cooling on the idea and it is not known who German Chancellor Angela Merkel would support.
Meanwhile the prime minister of Luxembourg, Jean-Claude Juncker, also seen as a possible candidate, has told French newspaper Le Monde: "If I were called upon, I would have no reason to refuse to hear, on condition that there are ambitious ideas for the post backing it up."
The Conservatives oppose the treaty, which establishes the role of president, and still hope it will not be ratified.
At a press conference party leader David Cameron again refused to say what his party would do in power, if it was already in place.
He said he would wait until that happened but added: "Maybe that time is coming closer. We will have to see."
Asked if he had spoken to European leaders about his opposition to Mr Blair's candidacy, Mr Cameron said shadow foreign secretary William Hague had made the party's position "very clear".
I think I can see what sort of president Tony Blair would be
"Everyone in Europe knows what we think about the role of president and about Tony Blair's candidature," he said.
He said the new role would take Europe "too far in creating the emblems of statehood rather than being about co-operation and co-ordination".
But he said if there was to be a president he would prefer it to be a more "chairmanic" role "rather than some all-singing, all-dancing, all-acting president and I think I can see what sort of president Tony Blair would be".
Mr Hague reportedly told Berlin and Paris that the Tories would take Mr Blair's appointment as a "hostile act" against a future Conservative government - which Mr Cameron did not deny.
And Green Party leader and MEP Caroline Lucas said the idea that Mr Blair should take on the role was "absurd".
"Can there be anyone outside of the government who really believes that the man who snubbed the EU over Iraq and joined with George W Bush to lead us into an illegal war is now the right person to become the EU's first Council President?" she said.
British ministers have been talking up the former PM's credentials, ahead of a summit of European leaders in Brussels later this week.
Foreign Secretary David Miliband said: "It's not a time for shy retiring violets... Europe needs a strong, persuasive, articulate advocate."
But former foreign secretary Lord Owen criticised Mr Blair's handling of the Iraq war: "I believe that disqualification from high office follows if you do not tell the truth to the House of Commons on a very serious question like going to war."
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