Colleagues of German comedian Jann Boehmermann have demanded that public broadcaster ZDF republish a satirical poem about Turkish president Recep Tayyip Erdogan that has sparked an investigation by German prosecutors.

In an episode of a topical comedy programme broadcast earlier in April, Boehmermann read out the poem, which contains several personal insults and mocks Erdogan for clamping down on freedom of speech.

The following day ZDF removed the poem from the recording of the show on its website, and prosecutors launched an investigation into Boehmermann after Turkey registered a formal complaint, and Erdogan demanded Germany bring charges for personal defamation under an obscure German law prohibiting insulting foreign leaders.

But the broadcaster's editorial committee has sent an open letter to channel directors, asking them to republish the poem, Spiegel reported.

"We would welcome the 'smear critique' [poem] being brought back to the media library from the poison cabinet, in order to document contemporary history," wrote the ZDF committee, and argue that modern societies ought to tolerate harsh satire.

Erdogan has sued thousands of people for insulting him since becoming Turkish leader, initially as prime minister, in 2003. In recent months, the German government has engaged in negotiations with Turkey in an effort to reduce the number of immigrants entering the EU, and critics have accused the German government and ZDF of buckling to pressure in failing to back Boehmermann.

In March, Turkey summoned the German ambassador in Ankara after German televison broadcast a satirical song about Erdogan, prompting Boehmermann to read out an even more savage critique of Erdogan on air.

Former Greek finance minister Yanis Varoufakis is one of several public figures to have signed a letter in Die Zeit condemning German authorities for launching an investigation into the poem.