High Representative Paddy Ashdown told reporters after the session that the fulfilment of criteria for association was non-negotiable.
Some European countries insist on the set criteria being met entirely, Ashdown added.
This primarily refers to the adoption of a law on the public radio and television network and the reform of the police, without which talks on stabilisation and association will not begin, he stressed.
Now it is all up to the authorities of Bosnia-Herzegovina, Ashdown said.
The PIC Steering Board called on politicians in the country, particularly those in the Serb entity, to start talks as soon as possible on the reorganisation of police forces as a precondition for the start of talks with the EU in autumn.
It also urged the Serb authorities to continue bringing to justice war crimes indictees wanted by the UN tribunal in The Hague.
Ashdown would not comment in detail on the fact that a dozen Serbs were arrested in eastern Bosnia in the past three days, only saying that this could be a very important development.
The local media have reported that several persons suspected of involvement in the 1995 atrocity in Srebrenica, including several active members of the Serb police, were arrested upon orders by the state prosecutor.