Turkey faces an uphill battle to secure visa-free travel in Europe for its citizens before July, with just two weeks to go to meet a number of conditions set by the European Union.

Ankara must reduce a backlog of asylum applications, grant all refugees access to its labor market, upgrade its visa regime to make it harder for people from countries with "a high migratory risk" to enter, and bring its data protection laws into line with EU standards, among other requirements, all by May 4.

The visa-waiver is part of a package of incentives the EU is offering Turkey to stop migrants piling into boats and making the dangerous voyage to Europe in search of sanctuary or jobs. The EU would also provide up to 6 billion euros ($6.8 billion) for Syrian refugees in Turkey and fast-track Ankara's EU membership talks.

Turkey's leaders are warning that the whole migrant deal will collapse if the EU fails to allow Turkish citizens visa-free short stays for travel or business purposes.

"If the European Union does not take the steps it needs to take, if it does not fulfill its pledges, then Turkey won't implement this agreement," Turkish President Recep Tayyip Erdogan said earlier this month.

But the bloc's executive European Commission insists the ball is in Ankara's court, even though Europe is desperate for Turkey to help stem the flow of migrants.

EU migration commissioner Dimitris Avramopoulos said Wednesday that there could be "no visa liberalization if not all benchmarks are met."

He said Turkey has been making good progress, but suggested that even this pace might not be quick enough.

"If we continue working like this most of the benchmarks will be met," Avramopoulos said.

"Every minute counts," he said. "We do not have much time in front of us."

The European Commission will present a new visa liberalization report on Turkey on May 4. If Ankara has met the 72 conditions that all visa-waiver countries must respect by then, the commission will propose that Turkey be put on the visa-free list. EU nations have promised to endorse that decision by June 30, almost 18 months before the original schedule.