A Swedish MEP has called for asylum seekers arriving in the European Union (EU) to be assigned a destination country rather than have free choice.

Her call comes as the European Commission warned member states that it will make full use of its powers to force them to comply with a programme designed to more evenly spread asylum seekers across the EU if they are not willing to do so voluntarily.

In a bid to stop migrants piling up in first port of call countries such as Greece and Italy, the Swedish Liberal MEP Cecilia Wikström has been tasked with steering reforms to the EU’s Dublin Convention on asylum seekers through the European Parliament.

Current EU rules state that asylum seekers must claim asylum in the first EU member state they reach. Consequently, some 160,000 migrants are currently stranded in Greece and Italy, the most common entry points to the EU.

Last year, the Commission drew up plans to relocate some of those migrants to other member states, but on Thursday admitted that just 13,546 people been relocated so far – 3,936 from Italy and 9,610 from Greece.

While Finland and Malta are on track to meet their targets for relocations, Hungary, Austria, and Poland have refused to take part in the scheme at all. The Czech Republic, Bulgaria, Croatia, and Slovakia are dragging their heels over taking in migrants, the Commission said.

Meanwhile, the migrants who continue to flock to favoured member states such as Germany are avoiding registering at their first point of entry into the EU to escape being returned there under existing rules.

Wikström hopes to even out the distribution of migrants with a new programme of targets based on automatic distribution. She also anticipates that a shared database will side-step the point of registration issue.

Writing for the Swedish newspaper Dagens Nyheter, Wikström commented: “A distribution scale is being drawn up based on GDP and population, in which every country’s share of the responsibility is clear. When a member state fulfils its part of the joint responsibility, asylum seekers that arrive there would be distributed to other countries.”

At a press conference on Thursday, the Commission warned that failure to show solidarity over the migrant crisis would result in penalties – likely to be fines – for member states.

Commissioner for Migration, Home Affairs and Citizenship Dimitris Avramopoulos said in a statement: “Responsibility cannot be fairly shared without solidarity. All our measures are interlinked, and member states cannot cherry-pick what they deliver on.

“It is up to member states to act and deliver on their obligations to ensure that all those eligible are relocated in time.”

Speaking to reporters, he added: “If we don’t have tangible efforts by September… the Commission will not hesitate to make use of its power.”