When debate on the treaty began, the SDKU party of Mikulas Dzurinda, a former prime minister, along with the ethnic Hungarian SMK and the Christian Democrats said they would abstain from the vote to protest against the media bill.
Pal Csaky, the SMK chairman, told the assembly on behalf of the three opposition parties: "The opposition must leave to show who is responsible for the eventual fiasco."
Vote on treaty
MPs were scheduled to vote on the treaty on Wednesday, but parliament can adjourn the motion. All 27 EU member parliaments must ratify the treaty for it to come into force.
At least five of the opposition's 65 deputies will have to back the treaty, as a 90-vote majority in the 150-seat assembly is needed for its approval.
Last week, the Organisation for Security and Co-operation in Europe criticised Slovakia's media bill, which it said would curb press freedom by letting the government fine media outlets if it judged them to be promoting "socially harmful" behaviour.
New press code?
Robert Fico, the country's prime minister, who has clashed with the media since winning elections in 2006, said he would not withdraw the new press code, which is also on the current parliamentary agenda.
Fico said: "The government ... sees no reason to link the ratification of the vital European reform treaty with the proposed media law. This is blackmail, to which the governing coalition will never surrender."
The reform treaty, signed by EU leaders in December, will allow more decisions to be taken by majority voting, notably on justice and security issues, and give more say to the European and national parliaments.