Turkey is now willing to accept the liberalisation of travel visa rules with the European Union by the end of the year instead of October, as previously targeted, the German newspaper Welt am Sonntag said on Sunday, citing senior Turkish government sources.

Ankara had threatened to walk away from an EU migrant deal should it not get more relaxed travel rules in October, but Turkey's EU Affairs Minister Omer Celik downplayed that prospect on Saturday after a meeting with EU officials.

Welt am Sonntag quoted senior Turkish officials familiar with the EU talks as saying that a delay until November or December was now seen as acceptable. However, Turkish officials were still insisting on securing visa liberalisation "no later than the end of the year," the newspaper said.

The newspaper also quoted EU sources as saying the two sides had narrowed their differences about implementation of Turkey's anti-terror laws, which the EU has set as a condition for granting Turks visa-free movement, but gave no details.

The EU, which depends on Ankara to curb the flow of migrants into the bloc, is now seeking to ease tensions with Turkey after criticising President Tayyip Erdogan's post-coup crackdown.

Celik said on Saturday Ankara would stick to the migration accord but it was "not rational" to expect Ankara to relax its counter-terrorism laws now as it fights Islamic State in neighbouring Syria and Kurdish militants on its own soil.

The EU worries Turkey applies its anti-terror laws too broadly in order to go after critics of Erdogan. – Reuters