Jan Boehmermann recited the poem, which made sexual references to President Recep Tayyip Erdogan, on television.
The Turkish government demanded last week to have Boehmermann prosecuted for insulting a foreign leader. Under German law, Merkel had to accept the request to approve a potential prosecution.
However, Merkel claimed that the approval “means neither a prejudgment of the person affected nor a decision about the limits of freedom of art, the press and opinion.”
She said the courts will have the final say, and it was up to prosecutors to decide whether the comedian should be taken to trial, according to the BBC.
Merkel also vowed to repeal the German law criminalizing insults of a foreign leaders by 2018.
The chancellor also expressed “great concern” about the state of media freedom and the fate of individual journalists in Turkey, as well as limitations on rights to demonstrate.
The comedian read the poem on ZDF television two weeks ago, in which he described the Turkish president as “stupid, cowardly and uptight” before making crude sexual references. ZDF argues that it didn’t break the law, while Boehmermann was given protection by police earlier this week after security concerns.
The German government had previously defended the poem as freedom of speech, but distanced itself from its previous remarks, saying it was “deliberately offensive.”
The Turkish president has been criticized for harassing journalists and attacking foes, while Merkel is under fire for compromising freedom of speech.
“That Erdogan’s arm now ultimately reaches to Germany, and via the chancellor, is unacceptable,” said lawmaker Dietmar Bartsch.
He also said Merkel’s credibility had been damaged.
Under the German law, individuals may be subject to up to three years in prison for insulting a foreign head of state.
The Associated Press contributed to this report.