Tony Blair is a contender to become the first president of the EU with the full backing of the British government, the new Europe minister said today.

Glenys Kinnock, in Strasbourg for the opening session of the new European parliament, said that although the former prime minister had not formally declared his candidacy, it was "certainly" the government position to support him.

"I am sure they would not do it without asking him," Lady Kinnock said. "The UK government is supporting Tony Blair's candidature for president of the council."

The new post is to be created under the Lisbon treaty, which will streamline the way the EU is run if it is endorsed in an Irish referendum in early October.

Blair would be the first sitting president of the EU, who will be appointed by European government chiefs for a minimum of 30 months and a maximum of five years.

If the Irish back the treaty on 2 October, EU leaders are expected to decide on who will get the presidency at a summit at the end of that month.

"Blair is seen by many as someone who has the strength of character, the stature," Kinnock said.

"People know who he is, and he would be someone who would have this role and step into it with a lot of respect and I think would be generally welcomed."

While Blair has declined to declare himself as a candidate before the outcome of the Irish referendum, Kinnock's remarks were the first solid confirmation that he is to run for the job.

However, British diplomats said her comments remained speculation for the moment because the Irish could yet vote down the treaty – as they did in their first referendum last year.

"The reality is Lisbon has not entered into force," one diplomat said. "Blair has yet to say whether he will stand."

A spokesman for the ex-PM said: "The job doesn't exist, so there is nothing to be a candidate for."

If he stands for the post, the founder of New Labour could yet in to stiff opposition in Europe.

Fredrik Reinfeldt, the Swedish prime minister – who took over the rotating presidency of the EU this month and will chair the October summit – is known to be strongly opposed to a Blair presidency.

Reinfeldt told the Guardian he would not get into any discussion about names for the post, while a senior European diplomat said the presidency would be "the absolute top subject" at the October summit.

Reinfeldt said he expected to oversee the launch of the Lisbon treaty, "including the elected council chairman [Europe president]".

He added that if the treaty was ratified by all member states, he expected "very many names" to be put forward for the presidency.

José Luis Rodríguez Zapatero, the Spanish prime minister, who will succeed to the EU presidency after Reinfeldt in January, is also an opponent of Blair.

France's president, Nicolas Sarkozy, an early fan of the idea of President Blair, appears now to have turned lukewarm.

William Hague, the shadow foreign secretary, said the creation of a new EU president "could be enormously damaging for Europe".

"Any holder is likely to try to centralise power for themselves in Brussels and dominate national foreign policies," he said.

"In the hands of an operator as ambitious as Tony Blair, that is a near certainty. He should be let nowhere near the job.

"It shows what a grip Lord Mandelson now has over Gordon Brown that he has been forced to support his bitterest rival."