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HANGZHOU, China, Sept 4 (Reuters) - German Chancellor Angela Merkel struck an upbeat tone after meeting Turkish President Tayyip Erdogan on the sidelines of the G20 summit, and said she expected progress on two thorny issues that have marred German and European ties with Ankara.

Both Germany and the EU, which depend on Ankara to keep a lid on the movement of migrants to the bloc, are trying to ease tensions with Turkey after criticising Erdogan's crackdown on opponents following the failed coup in July.

Merkel said she was hopeful that the European Union and Turkey could resolve their differences over visa-free travel for Turks, but an agreement was likely still several weeks away.

"The discussions with the European Commission are very intensive and are continuing," she said.

Merkel also said she expected a resolution in Germany's dispute with Ankara over visits to an air base in Turkey. She and other German officials have insisted that Ankara must end its ban on German lawmaker visits to 250 German soldiers working at Incirlik Air Base as part of the U.S.-led coalition's air strikes against Islamist State targets.

"I believe it is possible that we will get positive news on the justified demand in the coming days," the German leader told reporters after meeting with Erdogan in the eastern Chinese city of Hangzhou.

Turkey banned German lawmakers from visiting the base near the Syrian border in June after the parliament passed a resolution declaring the 1915 massacre of Armenians by Ottoman forces a genocide. German lawmakers in turn threatened to end the military mission there.

Turkey accepts many Christian Armenians were killed but contests assertions that up to 1.5 million died, and denies the killings were orchestrated.

Rainer Arnold, defence spokesman for the Social Democrats in parliament, told Reuters earlier he expected Turkey to approve an Oct. 4 visit by lawmakers to the base next week.

The EU worries Turkey applies its anti-terror laws too broadly to go after Erdogan critics and has made easing them a precondition for granting Turks visa-free movement.

Ankara previously threatened to walk away from cooperation on migration should it not get more relaxed travel rules in October, but now appears willing to push the deadline to the end of the year, the Welt am Sonntag newspaper reported.

Merkel said she and Erdogan also agreed that the political process aimed at ending the fighting in Syria must be resumed since the situation in Aleppo was unacceptable and a ceasefire was urgently needed.

(Reporting by Gernot Heller and Andrea Shalal; Writing by Andrea Shalal; Editing by Raissa Kasolowsky) ((andrea.shalal@tr.com; +30 2888 5159; Reuters Messaging: berlin.newsroom@thomsonreuters.com;))