* Mogherini says was first to support Turkish government in coup
* Says differences on Cyprus could be overcome in months
* Hahn says talks to upgrade customs union should start in 2017

Two of the European Union's top officials sought to smooth fractious relations with Turkey on Friday, vowing deeper trade ties and continued cooperation on migration, but there was no immediate end to a deadlock over visa-free travel for Turks.

The visit by EU foreign policy chief Federica Mogherini and Enlargement Commissioner Johannes Hahn comes almost two months after a failed coup which tested Turkey's relationship with the 28-member bloc it aspires to join.

Many Turks were incensed by what they saw as Europe's failure to show speedier solidarity over the July 15 putsch, in which more than 240 people died, accusing it of xenophobia and hostility to President Tayyip Erdogan.

"I was, I think, the first in those dramatic hours to communicate publicly the need to strongly defend and support the democratically elected institutions," Mogherini told a joint news conference with Turkey's foreign and EU ministers, defending Brussels' reaction to the events.

Turkey has long aspired to join the EU, but has accused Europeans of blocking progress because of bias against the Muslim nation. European officials have said Turkey still falls short of EU demands on basic rights and freedoms.

Mogherini said the talks in Ankara had been "frank, open, respectful and constructive", touching on issues including deepening a customs union and supporting Turkey as it copes with an influx of some 3 million Syrian refugees.

She said both sides had agreed to "talk more to each other and a little bit less about each other".

One of the biggest obstacles in Turkey's relations with the EU is Ankara's refusal to recognise EU member Cyprus, the Mediterranean island divided for four decades between the Turkish-controlled north, recognised only by Ankara, and the Greek Cypriot south, which has international recognition.

"We see a window of more than hope for this issue to be solved ... in the coming months," Mogherini said, adding both Turkey and the EU had a common interest in a solution.

But there appeared less hope of an immediate solution to the deadlock over a deal to grant Turks visa-free access to Europe by October. Brussels first wants Turkey to change its anti-terrorism law, which it deems too broad for European standards.

Turkish Foreign Minister Mevlut Cavusoglu said a concrete roadmap needed to be agreed for the deal, but Hahn said the timing would be up to the Turks.

Turkey says its anti-terrorism law is needed to fight threats from Islamic State and Kurdish militants. The EU says the law has been used too broadly, pointing to the prosecution of journalists and academics.

Hahn also said that internal preparations for discussions on upgrading a customs union with Turkey should be finalised by the end of the year and that negotiations should start in 2017.

Turkey wants to upgrade its 20-year customs union with the EU to include agriculture and services. That could nearly double its trade with the bloc to $300 billion and make it the EU's third-largest trading partner, officials have said.