The German government believes that Turkey finances terrorist organisations such as Hamas and armed Islamist groups in Syria, a leaked document shows.

"The many expressions of solidarity and support actions by the ruling AKP and President Erdogan for the Egyptian MB (Muslim Brotherhood), Hamas and groups of armed Islamist opposition in Syria emphasise their ideological affinity with the (broader) Muslim Brotherhood,” the ministry of interior wrote in reply to a question by left-wing party Die Linke,

Muslim Brotherhood is an Islamic organisation in Egypt, which came to power following the Egyptian revolution in 2012 but was removed in a coup a year later.

It is considered a terrorist organisation by Egypt, but not by the EU and US.

Hamas is an Islamist militant group controlling the Gaza Strip, a section of Palestinian territory which lies between Israel and Egypt. It is considered a terrorist organisation by the EU and the United States.

The document also reportedly claims that Ankara has recently deepened its links with these groups, up to becoming "the central hub for Islamist groups in the Middle East region as a result of the gradually Islamicised domestic and foreign policy of Ankara since 2011”.

It also said that a fourth of German nationals who travelled to Syria to join Islamic State or other jihadist groups, the so-called foreign fighters, were of Turkish origin.

The ministry of interior had asked to keep the document secret.

Germany is home to the largest Turkish diaspora in the world with roughly 3 million people of Turkish heritage living in the Bundesrepublik.

But relations between the two counties have soured since the parliament voted to recognise the massacres of Armenians by Turkish Ottoman troops in 1915 as genocide.

They suffered fresh controversy when chancellor Angela Merkel allowed for German comedian Jan Boehmermann to be prosecuted for having insulted Turkey’s president Recep Tayyip Erdogan.

They have also deteriorated after the botched coup attempt of 15 July, which Ankara says was masterminded by an elderly Islamic teacher, Fethullah Gulen, living in the US.

Germany condemned the attempt to seize power by military means. But it also fretted that Turkey’s post-coup purge of Gulen loyalists is spreading to German cities.

Gulen-linked businesses in Germany have been pestered by Erdogan supporters. German-based Turkish mosques have also read out a sermon accusing Gulen that was sent to them by a religious authority in Ankara, reporting to the Turkish prime minister’s office.

German politicians of different colours have urged Turkish-German citizens to identify with Germany, rather than Turkey, and not to take part in the purge.

Meanwhile, a poll last week showed that the majority of Germans would like to stop Turkey’s EU membership talks.

Accession talks aside, the EU and Turkey in March struck a deal to curb irregular migration in return for visa-free travel for Turkish nationals and other perks.

Germany's European affairs minister Michael Roth, a Social Democrat, said on Tuesday that it would be difficult to fulfil the five remaining criteria that would grant Turkish citizens visa-free travel to the EU in October, as planned.

But German finance minster Wolfgang Schaeuble, from Merkel’s centre-right CDU party, said that Germany must continue working with Ankara to uphold the migrant deal.

"I absolutely don't like what Erdogan is doing, but I don't agree that ... we should end cooperation with him," Schaeuble said.

"It is in our own interest to keep working together.