Newer EU member states must not be sidelined by the more established ones, UK prime minister Tony Blair and Hungarian leader Ferenc Gyurcsany say.
The leaders wrote a joint article for a Hungarian newspaper
In a joint article for a Hungarian newspaper, they said there should be no distinction between the 25 members.
BBC correspondent Guto Harri says many will assume the message is directed at France and Germany - the traditional driving force of the EU.
Mr Blair has been in Budapest for a conference with centre-left leaders.
The joint article stresses that old members have to demonstrate to the new that the union belongs to them and that the steps and sacrifices taken along the road to membership are appreciated.
It warns against any attempt to carve out new divisions that divide Europe into inner and outer cores.
In a speech at the Progressive Government Conference on Thursday, Mr Blair urged Europe and the United States to work together and develop a "common agenda" on the key international issues.
It was "simply wrong" that a "coherent international agreement" could be built on a "division between Europe and the US", he told the assembled leaders.
He warned there was a danger that progressive parties defined their economic policy by anti-globalisation and its foreign policy by anti-Americanism.
"Our task is not to stop globalisation but to make it work for the benefit of all the people not the few," said Mr Blair.
He and fellow leaders from about 13 other countries faced questions from delegates before attending a private working dinner on Thursday evening.
Spanish prime minister Jose Luis Rodriguez Zapatero, who pulled his troops out of Iraq after his surprise election victory in March, have also been at the summit, along with Canadian prime minister Paul Martin and Sweden's prime minister Goeran Persson.
The gathering was organised by think tank Policy Network, which is chaired by incoming EU trade commissioner Peter Mandelson.
It brings together 100 leading strategists and policy makers from across Europe and aims to discuss the renewal of the left in Europe and the world.