Turkey on Thursday confirmed it would hold new membership talks with the European Union next week and would pressure the bloc to "keep its promises" over visa-free travel.

Foreign Minister Mevlut Cavusoglu said he would hold talks with EU Commission Vice President Frans Timmermans on June 30, which would also be attended by Justice Minister Bekir Bozdag and EU Affairs Minister Omer Celik.

"We will go to Brussels to meet the EU Commission vice president and discuss the stalling on the visa exemption dossier, on the occasion of the opening of a new negotiating chapter," he said.

EU member states will meet on the same day to agree to open a new negotiating chapter with Turkey on finance and budget affairs in its membership bid, sources in Brussels said on Wednesday.

The question of Ankara's accession came up in Britain's bitterly-fought EU referendum campaign, with the high-stakes vote taking place Thursday on whether to stay or go.

Speaking ahead of the vote, an irate President Recep Tayyip Erdogan suggested Turkey could hold its own referendum on whether or not to continue the long-stalled EU accession process.

"We want to continue the discussions on the visa exemption. But the EU must also keep its promises and show its determination," Cavusoglu said.

A landmark deal agreed in March between Turkey and the EU had been expected to calm tensions and give new momentum to the Turkish membership bid.

But the EU says it cannot grant Turkey the key sweetener of visa-free travel to the passport-free Schengen zone if it does not narrow the scope of its anti-terror laws, something Ankara has refused to do as it battles Kurdish militants.

"In the current conditions, we cannot make any change in the anti-terror legislation," said Cavusoglu.

He also said that Erdogan's remarks on holding a referendum was "not blackmail or a threat".

"We are also under great pressure from our people who ask us what we are doing in a place where there is so much anti-Turkish sentiment."

"They want more action on our side and a revision if there is a stalling," he said.