BERLIN (Reuters) - German Foreign Minister Frank-Walter Steinmeier on Thursday announced he would visit Turkey next week and said it was important not to "slam the door" on Ankara despite Berlin's unhappiness over its post-coup crackdown.

The German parliament also voted 445 to 139 late on Thursday to extend German military support for the U.S.-led fight against Islamic State through the end of 2017, including deployment of over 250 soldiers at Incirlik Air Base in southern Turkey.

In a parliamentary debate in which he said he would visit Turkey on Nov. 15, Steinmeier said cutting off talks with Turkey about joining the European Union would hurt Turkish citizens as well as the government.

"If we slam the door now and throw away the key, then we will disappoint many people in Turkey who are looking to Europe for help and support, especially now," Steinmeier told lawmakers.

But Steinmeier repeated that reintroduction of the death penalty in Turkey would mean the "unmistakable end" of negotiations on Turkish entry into the bloc. He said Berlin would continue to press Ankara to respect the rule of law.

Turkey has detained, dismissed or suspended more than 110,000 soldiers, judges, teachers, journalists and others in the aftermath of an unsuccessful putsch by rogue military last July.

Turkish Prime Minister Binali Yildirim has said a "limited measure" could be drafted to restore the death penalty, which was formally abandoned in 2002, and President Tayyip Erdogan has said he would approve such a measure if parliament backed it.

"We want good relations with Turkey, but the reality has changed and we have to adjust our policies accordingly," Steinmeier said.

Ties between Germany and Turkey are also strained over a vote by the German parliament in June labelling as genocide the 1915 massacre of Armenians by Ottoman forces, which had triggered Ankara to temporarily ban German lawmakers from visiting troops at Incirlik Air Base.

German lawmakers spoke critically about Turkey's actions and insisted on the right to continue to visit Incirlik Air Base before approving continued deployment of military resources to support the fight against Islamic State. Germany flies reconnaissance missions from the Turkish base with six Tornado fighter jets.

"Our solders are not at Incirlik because of Turkey, but rather to fight Islamic State," said Julia Obermeier, a member of the Christian Social Union, the Bavarian sister party of Chancellor Angela Merkel's Christian Democrats.

Steinmeier told lawmakers that Germany was taking steps to help strengthen Turkish civil society, and would try to enable Turkish academics, journalists and artists who could not work in Turkey anymore to continue their work in Germany.

(Reporting by Sabine Siebold and Andrea Shalal; Editing by Richard Balmforth; Editing by Richard Balmforth)