* Proposals are a response to Paris attacks
* Concern over Europeans going to fight in Syria (Updates with statement agreed)
By Adrian Croft and Barbara Lewis
BRUSSELS, Feb 12 (Reuters) - European Union leaders called on Thursday for stricter checks on travellers entering the passport-free Schengen area and greater information-sharing as part of a revamped counter-terrorism strategy following last month's Paris attacks.
Spain had suggested that the agreement governing the 26-nation Schengen zone might have to be amended to permit more border checks on people suspected of terrorist links after 17 people were killed in a wave of violence in France last month that began with an attack on satirical newspaper Charlie Hebdo.
EU leaders meeting in Brussels said more could be done under the existing rules to strengthen checks on travellers entering or leaving the Schengen zone without changing the agreement or undermining the right to free movement within the passport-free area, which covers much of western Europe.
"We agree to proceed without delay to systematic and coordinated checks on individuals enjoying the right of free movement against databases relevant to the fight against terrorism," the leaders said in a statement.
European Commission President Jean-Claude Juncker said the Commission saw no need to revise the Schengen rules for now.
EU governments want to prevent Europeans going to fight with Islamic State militants in Syria and Iraq, fearing that they could carry out attacks on their return to Europe.
At present, only about 30 percent of passports presented by travellers entering or leaving the Schengen area are checked electronically to see if they are lost, stolen or counterfeit, officials said. The aim is to move that closer to 100 percent.
Only random checks are made to see if travellers entering the Schengen area appear in a police data base because they are wanted by authorities or suspected of terrorist links.
The 28 EU leaders also urged the European Parliament to adopt quickly a plan for countries to share airline passenger data.
Lawmakers have resisted endorsing the system for sharing data, known as the Passenger Name Record (PNR), on the grounds it would infringe people's privacy.
Under pressure to drop their opposition in the wake of the Paris attacks, the European Parliament pledged in a resolution on Wednesday to aim to finish work on the PNR law by the end of this year.
The leaders called for police to step up information sharing and for closer cooperation between EU members' security services and in the fight against arms trafficking.
They urged EU governments to quickly implement stronger rules to prevent money-laundering and terrorist financing and to effectively freeze assets used for financing terrorism.
They urged governments to remove Internet content promoting terrorism or extremism. (Editing by Alastair Macdonald)