David Cameron was accused on Sunday of blackmail and threats as his attempts to stop Jean-Claude Juncker becoming president of the European commission put him at the centre of a power struggle for control of the European Union.

The prime minister was criticised for his tactics in the battle to stop the former Luxembourg politician getting the top job, following reports of him warning that the appointment could spark an early referendum and drive the UK out of the EU.

Cameron appears to be staking his reputation on stopping Juncker, as he fears the leading candidate would not allow the UK to negotiate a new relationship with Brussels to the satisfaction of Eurosceptics.

His gamble against Juncker gained another possible ally on Sunday, as the Italian prime minister, Matteo Renzi, described him as "one name … but not the name for the commission". Cameron has already gathered support from Hungary, the Netherlands and Sweden. There are also reports that François Hollande has cooled on Juncker since the victory of the anti-immigrant, anti-EU Front National in the European elections and would prefer a French candidate.

However, Juncker himself said he was still confident of getting the job and told the German newspaper Bild that European countries should not "let ourselves be blackmailed". A broad majority of European leaders support his candidacy, he said in the interview.

The key player in whether Juncker gets the job is Germany. Chancellor Angela Merkel initially appeared to retreat from the choice of Juncker, who is supported by her party's own pan-European grouping. However, she has since declared that she would back him following claims in the media that she was capitulating too easily to British demands. Leading German publications such as Der Spiegel, Bild and Frankfurter Allgemeine had published editorials condemning Merkel's wavering course and suggested that backtracking on the open nomination process in favour of a backroom deal would amount to deceiving the electorate.

According to a poll carried out by Der Spiegel before last week's elections, 78% of Germans believed the candidate of the biggest bloc in the European parliament should go on to become president of the commission.

Labour also criticised the prime minister's negotiating strategy, suggesting the threat made the UK appear weak and isolated in Europe. Cameron was simply "playing to the gallery of the Eurosceptic backbenchers in his own party, and making threats when instead he should be forging alliances", said shadow Europe minister, Gareth Thomas. "Since his Bloomberg speech David Cameron has failed to set out what changes he wants to see or to build the necessary alliances across Europe in order to deliver reform."

Cameron's alleged comments about a British exit from Europe, reportedly made in a private conversation on the fringe of a Brussels dinner on Tuesday, were leaked to Der Spiegel.

Downing Street has declined to comment on the report that Cameron has played his trump card by threatening a UK exit. However, sources insisted the prime minister is still committed to a referendum in 2017 and does not want to bring it forward. At no point did the he suggest the appointment of Juncker could destabilise the UK government, the source said, and he was simply went into Tuesday's dinner making it clear that appointing a face from the past could pose a risk to the stability of the EU.

That does not exclude the possibility that Cameron warned other national leaders he would be under pressure to hold an early poll if the EU ignores the rising Eurosceptic mood of the electorate, following a surge in nationalist parties at the European elections.

On Sunday, Conservative MPs said it was a pivotal battle for Cameron that could determine whether he is successful in his desire to get a new deal for Britain from Europe before holding a referendum before the end of 2017.

Bill Cash, a leading Eurosceptic and chairman of the Commons European scrutiny committee, said it would be catastrophic for Cameron if Juncker were appointed but a potential advantage to the Eurosceptics who want to take the UK out of the EU. "[Those who want to leave the EU] would then be able to demonstrate to the British people why it is that we need to change the nature of our relationship with the European Union," he said. Juncker is a federalist nightmare who is completely arrogant and totally fixated on future union, he added.

One Number 10 adviser also said the appointment of Juncker would make it much more difficult for Cameron to control his own party. "The Eurosceptics will seize on anything and try and push for an early referendum ... that would play into their hands. They will be secretly delighted if he gets the job," the senior MP said.

Negotiations between the European parliament and European council of national leaders are expected to continue throughout June, with the council announcing its candidate at the end of the month and MEPs casting their vote in July.

One of Downing Street's main aims has been to stall the process to allow other leaders to digest the results of the European elections and allow other candidates to emerge.

The controversy over Juncker comes as Tony Blair prepared to give a speech warning Europe that the rise of Ukip and other nationalist parties should act as a wake-up call.

The success of these parties has revealed a "deep anxiety, distrust and alienation from the institutions and core philosophies of Europe" that cannot be ignored, he said in comments released to the Times. In his speech, he will call for Britain to lead, not follow, in the debate about the future of the EU.

In a swipe at David Cameron's plans for a renegotiation and in/out referendum by 2017, Blair will call on pro-Europeans to "make the debate more than about the repatriation of certain competencies and rules".

He will say: "Even among those who are in favour of Europe, there is a keen sense that the moment is right for Europe to think carefully about where it goes from here, and how it reconnects with the concerns of its citizens and how it changes in order better to realise its ideals in a changing world.

"It has to be a debate elevated to a Europe-wide level, with Britain playing a leading role, not just a negotiation of Britain's terms of membership.

"It has to be about what is good for Europe as well as what is good for Britain."

The row over Juncker comes at a crucial time for the prime minister as he is under increasing pressure from Tory backbenchers to solidify his commitment to a referendum. A minority of backbenchers, including former leadership candidate David Davis, are pushing for an earlier referendum to convince those tempted by Ukip that he is serious about the issue.

There is also disagreement with the top cabinet ranks about how the party will manage to curb the immigration of EU citizens. Theresa May, the home secretary, has been pushing for much tougher restrictions amid signs she will fail to hit the net migration target.

However, some of her cabinet colleagues are reluctant to set up a clash with the EU as the EC has indicated the principles of free movement are non-negotiable. George Osborne, the chancellor, acknowledged this weekend the government would struggle to hit its target without changes in EU rules. Osborne told the Sun: "That [ambition] requires renegotiation of our membership of the EU, an in/out referendum so the British people have their say. The point that people need to focus on is that a general election is not a free hit. It matters who the government is."

The coalition has little chance of making progress on the issue of EU immigration as the Liberal Democrats are firmly opposed to undermining free movement. Lord Ashdown, the former Lib Dem leader, told the BBC's Andrew Marr Show that he would expect his party to block any Conservative immigration measures that would stop EU citizens having the right to move to the UK for work.