The former prime minister described the poll surge by anti-EU parties across the continent as a "wake-up call", saying it exposed "deep anxiety, distrust and alienation from the institutions and key philosophy of Europe", The Times reported (£).
In a keynote speech to the CBI on Monday, he said: "The victories of Ukip in the UK and the National Front in France and the election of parties across the continent on explicitly 'anti-the-status-quo in Europe' platforms signify something. They cannot be ignored.
"The election results matter. They are a wake-up call to Europe and to Britain. Our response in Europe, as in Britain, should be to lead, not follow."
The speech follows claims Blair is seeking a new role within the Europe debate.
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".
"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 intervention came with Cameron embroiled in a damaging stand-off over who should take over as the next president of the European Commission.
According to Der Spiegel magazine, Cameron told his counterpart: "A figure from the 80s cannot resolve the problems of the next five years."
Downing Street has declined to comment on the contents of the "private conversation", but Cameron has already made clear his bitter opposition to Juncker's appointment.
This drew a sharp response from the former Luxembourg prime minister, who expressed confidence that he would secure the post this summer with support from Merkel and the European People's Party (EPP) bloc that still dominates the European parliament.
"Europe must not allow itself to be blackmailed," Juncker told Germany's Bild am Sonntag newspaper.
The row heaps further pressure on Cameron in the wake of a mauling from Ukip at the local and European elections, and with just days to go until a crucial by-election in Newark.
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Polls have suggested Nigel Farage's party is close to overturning the 16,000 majority the seat's disgraced former MP Patrick Mercer won in 2010 - potentially dealing a hammer blow to the Tories.
Cameron has ordered his ministers to visit the constituency at least three times during the campaign - and is expected to make a fourth trip himself imminently.
In a sign of Conservative nerves over the growing threat from Ukip, Iain Duncan Smith has attacked the BBC for failing to give due prominence to Mr Cameron's pledge to hold an in-out referendum by 2017.
He also stressed that the PM knew he had to negotiate "significant return of powers" in order for Tory colleagues to vote to stay in the union.
Duncan Smith told the Sunday Telegraph he wanted to limit migration from the EU, arguing that Brussels should be stripped of control over who is entitled to state benefits in Britain.
Meanwhile, Chancellor George Osborne has blamed European rules for the Government's failure to control immigration, conceding for the first time that Cameron's target of bringing net migration levels below 100,000 by next May will not be met.
Official figures showed the number coming to the UK for at least a year, minus the numbers leaving, rose 58,000 to 212,000 in the year to September 2013.
Cameron has rejected calls to drop the target, arguing it is still "achievable" but refusing to offer a "cast iron guarantee".
But Osborne told the Sun on Sunday that the goal could not be achieved until the terms of Britain's EU membership have been changed.
"We have got our policy, we are delivering on the policy, and the key dimension to it which we need to now deliver on is the European aspect," he said.
"That requires renegotiation of our membership of the EU, an in-out referendum so the British people have their say."
Defence minister Anna Soubry also admitted it "does not look like" the net immigration target will be achieved.
But she risked provoking a backlash by saying some of the concerns she heard about immigration were "frankly racist".
"When you make the case with people who come and see me in my constituency surgery who say I'm really worried about immigration. You say really, why? This is Broxtowe. We don't have a problem with immigrants," she told the BBC's Andrew Marr show.
"When you explain all that to them they get it. Not all of it. Some people have prejudices, some people are frankly racist, but there are many who just don't know the argument."
Former Liberal Democrat leader Lord Ashdown added to Tory woes by signalling their coalition partner was likely to block proposals for tightening immigration rules - thought to include restrictions on employing cheaper foreign workers and provision to deport unemployed Europeans after six months.
"It is unlikely that we will let those go through. But let's have a look," Lord Ashdown said.
"Immigration is intensely valuable to Britain... we have benefited hugely from immigration in this country."
Ed Miliband was also facing calls from Labour MPs to take a tougher line on immigration, with a group including former minister Frank Field and prominent backbencher John Mann writing to the Observer urging tighter restrictions for new EU states.Suggest a correction