The dispute assumed decidedly nasty proportions when Erdogan and some other Turkish officials began comparing the modern German government to Nazi Germany.
PEN said the charges against Akhanli relate to activities conducted while he was outside of Turkey.
This seems to be the latest diplomatic shot fired between the two countries in an increasingly strained relationship. They soured further after Turkey arrested 10 human rights activists, including the director of Amnesty International and a German citizen, in July.
Upping the stakes in a intensifying row with Berlin, Erdogan said ethnic Turks in Germany should not cast their ballots either for Merkel's Christian Democratic Union (CDU), Gabriel's Social Democratic Party (SPD), or the Greens.
Chancellor Merkel responded immediately, saying that her government would "not stand for any kind of interference" from foreign governments in German elections.
Johanna Konta claims place in Cincinnati Open quarter-finals
Both face the prospect of a long day Friday - an early afternoon match and, if they win, another at night. She gained a second-set edge with a backhand victor on break point for a 4-2 lead before closing it out.
Addressing Merkel as "Madam", Erdogan said the Turkish authorities had sent Germany dossiers on 4,500 suspects wanted for extradition to Germany on terror charges and received no answer.
Turkish writer Dogan Akhanli who has been critical of Ankara's policies and has written extensively about the Armenian Genocide, was arrested on Saturday, August 19 morning in Granada after the Turkish government issued an Interpol worldwide arrest warrant, El Periódico reports. Community leader Atila Karaborklu accused Erdogan of wanting to divide Germany's Turkish communikty.
Gabriel's SPD - whose candidate for the chancellorship is ex-EU parliament speaker Martin Schulz - and Merkel's CDU are rivals in the election.
Ozdemir had previously pressed Ankara to recognise the World War I killings of Armenians as genocide.
There are an estimated three million Turkish-origin people living in Germany.