Europe Minister Geoff Hoon has admitted the EU has "an image problem" and must convince people in the UK that it "makes a difference to their lives".
Geoff Hoon was appointed Europe Minister in last month's reshuffle
The leaders of the 25 EU nations are meeting to discuss the direction they will take in the coming year.
Mr Hoon said people did not understand how events in Brussels affected them.
Foreign Secretary Margaret Beckett added the EU needed to "reconnect" with Europeans "wary" that their views were ignored in the policy-making process.
She said that by rejecting the EU's proposed constitution, voters in France and the Netherlands had sent "a very clear message".
This was "that the European Union needed to reconnect more closely with the people of Europe", who "were wary of a European Union that seemed to sets its own direction with minimal reference to what they actually wanted out of it", she said.
'Restart the debate'
Mr Hoon said his aim was "to restart the debate in this country" on how the EU should proceed, and "to ensure that the EU continues to deliver real outcomes on a programme designed to address the serious problems of the day".
He said people did not always see the "benefits and opportunities" that EU membership brought, partially blaming a "deeply sceptical" media and the "rabidly anti-European" Conservative Party.
He added Europe had benefited consumers and business, and the government had to continue "completing" the single market.
The public 'feel excluded' from the EU's decision-making process
However, William Hague, the shadow foreign secretary, blamed a lack of transparency for an inability by the EU to connect with voters.
"First, national parliaments and electorates cannot hold ministers to account if it's not clear how they've acted in the council.
"Secondly, it is easy for governments to blame Brussels for decisions they might themselves have agreed to and, thirdly, closed meetings can result in deals which no government fully accountable to its own parliament would have agreed to."
Mr Hague said the Council of the European Union and the North Korean assembly were the only legislatures in the world which now met in secret.
UK 'must engage'
Mr Hague mocked ministers in the Commons on Wednesday for deciding that a further "period of reflection" was needed before deciding what to do about the European Constitution.
The president of the European Commission, Jose Manuel Barroso, said it was clear that there was a need "more than ever, to change some rules of decision-making inside the European Union".
"If we want to expand further it's obvious that we need more than ever to change the rules," he said.
EU leaders are expected to postpone a decision on what to do with their constitution, probably until 2008, but appear likely to press ahead with enlargement.
Meanwhile Conservative MEP Richard Ashworth questioned whether the time and money spent on the summit is justified.
He claims several important issues have been omitted from the agenda, which he alleged amounted to "negligence" on the part of Austria, which currently holds the rotating presidency of the EU.
He was also unhappy the meeting was scheduled during the World Cup. Tony Blair will arrive late in order to watch England's match against Trinidad and Tobago beforehand.