The Turkish government has demanded that a German comedian who wrote a poem insulting President Recep Tayyip Erdogan be punished, calling the verses a "crime against humanity".

Jan Boehmermann fuelled a diplomatic spat between Germany and Turkey late last month when he read out a poem on television lampooning the Turkish head of state as "a professional idiot, cowardly and uptight" and accusing him of performing sex acts with animals.

The poem was not just insulting Erdogan, but all 78 million Turks, Deputy Prime Minister Numan Kurtulmus said in the south-eastern Turkish city of Sanliurfa on Monday.

"This is why we as the Republic of Turkey want this insolent man to be punished immediately under German law for insulting a president," he said.

He accused Boehmermann of having committed a "serious crime against humanity" with his poem.

The verses had "crossed all lines of shamelessness," he said.

However, Kurtulmus insisted that Turkey did "absolutely not want to put political pressure" on Germany.

His comments came as German government officials met to decide how to respond to a request from Turkey to prosecute the comedian.

Public prosecutors in Mainz have already launched a preliminary investigation into Boehmermann and public broadcaster ZDF to determine whether the poem violates a law that criminalises insults against representatives of foreign states.

A controversial deal the European Union struck with Ankara to return migrants from Greece to Turkey has given Erdogan political leverage in his dealings with the bloc.

Rights groups insist the country's campaign against the Kurdish minority in the southeast and its crackdown on the Turkish press should not be ignored as the EU struggles to get on top of the migration crisis.

German government spokesman Steffen Seibert said on Monday that official consultations on Turkey's request would last several days, adding that freedom of speech and artistic expression was a non-negotiable right both domestically and in relation to other countries.