Two German footballers of Turkish heritage posing for photographs with the Turkish president, Recep Tayyip Erdoğan, have reignited a debate over dual citizenship and national identity in Germany, as the country embarks on a bid to defend its World Cup title.

Midfielders Mesut Özil and Ilkay Gündoğan, who currently play for Arsenal and Manchester City in the Premier League and are both set to represent their birth country at the tournament in Russia this summer, were criticised by politicians including the chancellor, Angela Merkel, for meeting with Erdoğan during his visit to the UK.

In a meeting at London’s Four Seasons hotel on Sunday evening, which was also attended by German-born Everton striker Cenk Tosun, the players handed signed club shirts to the leader of Turkey’s Justice and Development (AKP) party. The shirt given by Gündoğan, who holds German and Turkish passports, bore the message: “To my president, with my respects.”

The pictures amount to a PR coup for Erdoğan, who is seeking to extend his 15-year rule in a snap poll on 24 June but is banned from holding election campaign rallies on German soil. About 1.2 million people in Germany with a Turkish background are eligible to vote in the election.

Diplomatic relations between Germany and Turkey were already frayed over the one-year imprisonment of recently released German-Turkish journalist Deniz Yücel. But the backlash to the incident has been even louder because Özil and Gündoğan have both been championed as successful examples of Germany’s policy of cultural integration.

World Cup winner Özil was awarded an “integration” prize by the Hubert Burda Media group in 2010. That year the president of Germany’s football association (DFB) had complained about politicising football after Merkel made an unscheduled visit to the Germany changing room following a 3-0 win over Turkey. Photographs of the German chancellor shaking goalscorer Özil’s hand were distributed by the government to the press afterwards.

Facebook Twitter Pinterest Photograph: Kayhan Ozer/AFP/Getty Images

Facebook Twitter Pinterest Photograph: Anadolu Agency/Getty Images

After Sunday’s incident, the chancellor’s spokesperson Steffen Seibert said the situation had “thrown up questions and invited misunderstandings”, while DFB chief Reinhard Grindel said in a statement that it was “not a good thing” for the players to pose with Erdoğan.

“The DFB of course respects the special situation for our players with migrant backgrounds, but football and the DFB stands for values that Mr Erdoğan does not sufficiently respect,” Grindel said.

While Arsenal star Özil has not commented on the affair, Gündoğan has defended the meeting as a “gesture of politeness” that he had made “out of respect for the president’s office”. Critics say Gündoğan could have shown his respect without allowing himself to be used as a political tool, pointing out that Liverpool FC’s Germany international Emre Can had reportedly declined an invitation from Erdoğan’s team.

Germany team manager Joachim Löw has emerged as one of the few forgiving voices in the debate, saying people with a migrant background sometimes had “two hearts beating in their chest”, which “wasn’t always quite so easy to reconcile”. Löw said he had not hesitated “for one second” about including the two players in his provisional 27-man squad.

Some journalists and rightwing politicians had called for Özil and Gündoğan to be kicked out of the national side. Sebastian Münzenmaier, an MP for the rightwing nationalist Alternative für Deutschland, said unless the two players stopped “flattering” the Turkish president, “the Turkish national side can look forward to two new players”. Football players cannot switch national teams after they have represented one country at senior level.