French President Francois Hollande has called for the EU to reduce its role "where it is not necessary".
Reacting to the spectacular success of parties such as France's National Front (FN) and the UK Independence Party (Ukip) in the European elections, Mr Hollande acknowledged that the EU had become "remote and incomprehensible" for many of its citizens.
"This cannot continue. Europe has to be simple, clear, to be effective where it is needed and to withdraw from where it is not necessary," he said in a televised address to the French nation.
Mr Hollande's comments will be greeted with delight by Eurosceptics who accuse Brussels of meddling in national affairs.
They will also be welcomed by the likes of British Prime Minister David Cameron, who also advocates a scaling back of the powers currently vested in the European institutions.
But the signal that France would consider a reversal of powers to national governments will cause concern among those, particularly in Germany, who believe European integration still has further to run.
Mr Hollande's Socialist Party suffered a humiliating setback in the elections for a new European Parliament, registering a record low vote of just under 14% while the FN topped the polls with nearly 25%.
The French leader stressed that France remained committed to playing a leading role in Europe, but also acknowledged that the economic austerity of recent years had damaged the cause of integration.
"I am a European, my duty is to reform France and to change the direction of Europe,” he said.
"Europe, in the past two years, has overcome the euro crisis but at what price? An austerity that has ended up disheartening the people."
Speaking about the results, Ms Le Pen told supporters: "The people have spoken loud and clear."
"They no longer want to be led by EU commissioners and technocrats who are unelected."
British Prime Minister David Cameron called EU leaders to discuss choosing a new European Commission president, his office said today.
The prospect of UKIP's widely forecast success may have influenced Cameron's plans to lobby against the two most prominent candidates for the commission's president, on the grounds that they are too federalist.
With a national election next year in the UK, the rise in UKIP's popularity has put Mr Cameron under pressure to toughen his stance on Britain's relationship with Europe, to win over voters and placate anti-EU members of his governing Conservative party.
EU leaders are due to hold a preliminary discussion about who should get the Commission job, and other senior EU roles, at an informal dinner in Brussels tomorrow.
"The prime minister has agreed with the other leaders that tomorrow's meeting is just the start of the process and there will need to be more consultation in the coming months," a spokeswoman for Mr Cameron's office said.
Earlier today, former Luxembourg Prime Minister Jean-Claude Juncker, the centre right's choice for Commission president, brushed off questions about his candidacy, saying the job was effectively his for the taking.
Candidates must be nominated by the EU's 28 heads of state and government and then be approved by a simple majority in parliament.
"It is clear that other leaders share the Prime Minister's view that the European Council has a clear mandate in the Treaty to nominate the next President of the European Commission and it is important to follow that procedure," the spokeswoman for Mr Cameron said.
