Brussels (AFP) - The EU on Wednesday gave conditional backing to visa-free travel for Turks under a migrant deal and unveiled new asylum rules including fines for countries that refuse their share of refugees.

In its latest bid to tackle the biggest migration crisis since World War II, the European Commission proposed making countries pay a "solidarity contribution" of 250,000 euros ($290,000) per refugee they decline to take.

Turkey has threatened to tear up a March agreement to take back migrants from Greece if the EU fails to keep its promise to allow nearly 80 million Turkish citizens to travel without visas to Europe.

Turkish Foreign Minister Mevlut Cavusoglu said visa-free travel could herald a "new page" in the often troubled relations between the EU and Ankara, but warned Brussels to "stick to its promise".

European Commission Vice President Frans Timmermans said the EU's executive arm would recommend the plan so long as Ankara meets the remaining criteria by the end of June.

Turkey still has five more benchmarks to go on the EU's list of 72 -- which include biometric passports and human rights issues -- despite making "impressive progress" in recent weeks, Timmermans said.

"There is no free ride here, and we are clear about what remains to be done," Timmermans told reporters, in response to criticism from several EU states that the deal is too soft on Turkey's rights record.

- EU parliament hurdle -

The 28 EU member states and the European Parliament must also approve the visa scheme, which is by no means a foregone conclusion.

MEPs on Wednesday demanded a "written guarantee" from the Commission that all steps had been fulfilled before it would vote, while Manfred Weber, head of the leading centre-right group in parliament, said it was "too early" for the visa proposal.

Under the plan, Turkish citizens would be allowed to make 90-day visits to Europe's 26-country Schengen passport-free area for business or tourism without needing a visa.

Also on Wednesday the Commission unveiled its long-awaited proposal for replacing its outdated asylum system with a mechanism for relocating refugees in a crisis.

The so-called Dublin rules currently in force have been criticised as obsolete and unfair to countries like Greece, the main entry point for the 1.25 million migrants who have entered the bloc since last year.

The arrival of a wave of humanity fleeing conflict in Syria, Iraq, Afghanistan and elsewhere has caused severe tensions in an EU already facing economic and strategic challenges.

Under the Dublin rules, migrants seeking asylum must lodge their application in the country where they first arrived, and should be returned there if they try to move elsewhere in the bloc.

Timmermans said the new mechanism would be activated only in times of crisis, and countries that show they temporarily cannot take any asylum seekers under the mechanism should show "financial solidarity", he added.

The Commission set the figure at 250,000 euros per asylum seeker.

- 'Blackmail' claim -

Hungary quickly dubbed the fines plan "blackmail". Its hardline Prime Minister Viktor Orban has led opposition from mostly eastern EU states to taking in more refugees.

Germany has led the way for the rest of the EU, in taking more than one million asylum seekers in 2015.

The EU last year approved a separate scheme to share out 160,000 refugees around the bloc but less than one percent of that number has been redistributed so far.

Brussels hopes the asylum reform will work in tandem with the EU-Turkey deal, as a result of which numbers of arrivals in Greece have dropped dramatically since it came into force on March 20.

Under the deal the EU also agreed to speed up Turkey's long-stalled membership bid in addition to promising visa liberalisation.

But many EU states still have concerns about the legality of the agreement and the human rights situation in Turkey, where an increasing number of journalists and critics of President Recep Tayyip Erdogan have been prosecuted.

Meanwhile the Commission further announced a six-month extension of border controls in the Schengen zone, which have been reintroduced in some places as a result of the migrant crisis and recent terror attacks in Paris and Brussels.

Germany, France, Austria, Denmark and Sweden requested the extension, saying the border situation remains "extremely volatile".

Since 2015 several countries in the Schengen zone have reintroduced border controls due to the migrant crisis -- effectively suspending its principle of border-free travel.

EU rules say countries can reintroduce border controls for up to two years, in periods of up to six months at a time, in exceptional circumstances.