(Reuters) – The European Union’s executive said on Wednesday it will propose on May 4 granting Turks visa-free travel to the bloc from late June in a deal under which it is to stop uncontrolled migration into Europe – provided Ankara meets the remaining conditions.

A first European Commission report on implementation of last month’s EU-Turkey agreement said good progress had been made but more resources and commitments were needed to carry out sustained returns of migrants from Greece to Turkey and to resettle Syrian refugees from Turkey directly to Europe.

The Commission did not say how many of the 72 benchmarks for visa liberalisation Turkey has yet to complete but it pointed to several areas where work remains to be done.

They include reducing a backlog of asylum applications, granting all refugees legal access to the labour market, strengthening visa requirements for countries that pose a high migration risk, taking necessary steps to protect fundamental rights and ending discrimination against citizens of EU member state Cyprus, which Turkey does not recognise.

Migration Commission Dimitris Avramopoulos, speaking to reporters, declined to say how many benchmarks Turkey now met but stressed that Ankara’s compliance was improving by the day.

“It’s not a question of number, it’s how quickly the process is going on,” he said, while repeating the Commission’s position that there could be no liberalisation until all conditions were fulfilled. “I believe that at the end, if we continue working like this, most of the benchmarks will be met.”

The EU executive also urged Ankara to improve readmission of Turkish nationals who overstay in Europe and are expelled, and of third country nationals from all EU member states, so that an EU-Turkey Readmission Agreement is fully effective from June 1.

Turkish Prime Minister Ahmet Davutoglu said on Tuesday that Ankara was fulfilling all the terms of the EU deal and if the Europeans did not meet their part, Turkey would stop applying its side of the bargain.

“The Commission will present its third visa liberalisation progress report for Turkey on May 4 and if Turkey takes the necessary measures to fulfil the remaining benchmarks, the report will be accompanied by a legislative proposal for transferring Turkey to the visa-free list,” the report said.

Separately, the Commission proposed easing visa requirements for Ukrainians, something it had promised for months as part of efforts to help Kiev in its confrontation with Russia. Avramopoulos said he hoped member states and lawmakers would endorse the proposals “very, very soon”.

Addressing concerns about immigration similar to those raised by the offer to Turkey, the Commission statement stressed that Ukrainians would not have a right to work in the EU.

“NO POLITICAL DISCOUNT”

The proposal must be approved by a weighted majority of EU governments representing at least 16 of the 28 member states and 65 percent of the EU population, and a majority in the European Parliament to take effect. It is disputed in Germany and France, where many fear a flood of Turkish migrants, although the change would not allow Turks to work or stay longer than three months.

German EU lawmaker Markus Ferber, from Chancellor Angela Merkel’s conservative Bavarian sister party, said Turkey should not be given any “political discount”.

“The burden of proof is not on the EU but on Turkey. There are clear conditions for visa freedom. The fact is that Turkey doesn’t meet them at the moment,” Ferber said in a statement.

On the implementation of the migration deal so far, the Commission said 325 irregular migrants had been returned to Turkey from Greece and 103 Syrian refugees resettled in the EU.

Greece has set up accelerated procedures to process asylum seekers on its Aegean islands, and the EU agencies for border management and asylum assistance have deployed escort officers, readmission experts, asylum officers and interpreters to help.

However, a 3 billion euro EU fund to support refugees in Turkey is still 390 million euros short and 12 of the 28 EU member states have yet to contribute.

“Member states need to step up their efforts in supporting Greece … More pledges and acceptances are needed in terms of resettlement, relocation and support to the EU agencies,” the report said.