The initiative to harmonise laws has been sped up after the attacks on the US and won new support among countries like the United Kingdom which might normally be suspicious of yielding sovereignty to the EU.
The basis of a new agreement will be consensus on what constitutes terrorism. The commission will put forward a broad definition, which includes cyber and environmental attacks.
It also hopes to lay down a Europe-wide agreement on maximum sentences which, in the most serious incidents, would be life in prison.
Warrants issued in one country for terrorist offences would be recognised by other EU countries and replace extradition, if the proposals are adopted.
"It will be the first time there will be automatic mutual recognition of judgments," said one official. "This is the first step in achieving European co-operation on justice."
EU policymakers see a big new role for Europol in combating international terrorism in the EU. At the meeting of Justice and Home Affairs Ministers they are expected to discuss the possible extension of Europol's mandate to allow it to work more closely with the authorities in the US.
British officials have promised that Jack Straw, the British Foreign Secretary, will be giving firm support to a new package of anti-terrorist measures.
Other ideas likely to be discussed tomorrow include mutual recognition of orders freezing the assets of terrorist suspects, and EU-wide lists of which terrorist groups should be banned organisations. In the wake of the attacks on America and the support offered by European countries, there may be a move to extend EU-US cooperation on counter-terrorism.
And there may be calls for all 15 member states to sign up to and implement the United Nations' International Convention for the Suppression of the Financing of Terrorism, which lays down cross-border procedures.
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