Firm opposition from France and Sweden forced Spain and Britain to scale down controversial demands to impose penalties on poor nations deemed not to be cooperating with measures to seal holes in the EU's outer borders.
However, agreement is expected on unified procedures for handling asylum applications.
British ministers are also predicting a pledge to implement the much-ignored requirement that asylum seekers have their applications processed in the EU country of arrival.
Before the summit ends on Saturday, leaders are eager to find a common strategy on immigration - an issue which has been key to the success of several far-right parties in a string of recent elections across Western Europe.
Other issues on the agenda include enlarging the EU to include 10 new members and changes to the way the union is run.
The summit got off to a late start to allow for delegations delayed by a widely-observed Spanish general strike on Thursday to reach the
conference centre - and to let them watch the keenly awaited England-Brazil World Cup match in Japan.
Car bombs believed to have been planted by Basque separatists exploded in the tourist resorts of Fuengirola and in Marbella on Friday, apparently to coincide with the summit.
French fury
Spain had argued for a tough line on immigration to ease Europeans' fears of being swamped by foreigners - concerns which have been exploited successfully by far-right and populist parties across the continent.
"Without a response from the European governments, it will be increasingly easy for political formations with a xenophobic approach to win public support," said Spanish Foreign Minister Josep Pique in an interview with El Mundo.
"Our response must be realistic and based on taking measures that aren't pleasant to adopt but which will produce essential results," he said.
But pressure from France in particular is thought to have forced a climbdown.
Along with Sweden and Luxembourg, France says it would be counter-productive, arguing that it would further impoverish countries and thereby increase the number of people wanting to leave.
"We must encourage, convince and cooperate rather than sanction," said French President Jacques Chirac.
"We cannot accept the principle of conditionality for aid. We
are opposed to any sanction on aid."
Spain had argued there was 95% agreement on its proposals for a Europe-wide immigration policy but admits that the idea of penalising countries because their people try to get into the EU has been a sticking point.
"We are now trying to draft a consensual proposal that would state that principle but would make it clear that the emphasis is not on sanctions, but on co-operation," said Mr Pique who described the disagreement with France as "semantic".
British cool off
UK Prime Minister Tony Blair - once a supporter of the idea - has also cooled off since one of his ministers described it as "morally repugnant".
"Let me stress that as far as EU aid is concerned we are not talking about anything whatsoever that would run counter to the fundamental aim of poverty reduction," he said.
But he said developing countries had a responsibility to participate in efforts to stem immigration.
However, Denmark, which takes over the rotating EU presidency from Spain in July, maintained its support for the hardline policy.
"I think we need a mechanism whereby countries agree to take back their own citizens who have illegally come to the EU," said Danish Prime Minister Anders Fogh Rasmussen.
The tone of the debate has caused concern among human right groups who complain that a "Fortress Europe" mentality is growing.
And they express concern that the EU's attempt to redefine the basis for granting refugee status to asylum-seekers would take away the safeguards for persecuted people in the Geneva convention.
Among the other immigration proposals to be discussed at the Seville summit are plans
"
I think we need a mechanism whereby countries agree to take back their own citizens who have illegally come to the EU
"
Danish Prime Minister Anders Fogh Rasmussen
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