The jailing of former NSW Labor MP Eddie Obeid underscores the case for a national anti-corruption body, federal MPs say.

Greens leader Richard Di Natale wrote to Labor leader Bill Shorten on Friday, calling for the pair to team up in 2017 and push for a federal ICAC-style body, a move the Greens have pushed for in the last three parliaments and under the last three leaders.

Senator Di Natale said in the letter that, in the Obeid case, "justice was only able to be achieved through investigative journalism, and delivered for the citizens of NSW because they have an Independent Commission Against Corruption overseeing the NSW Parliament and public service".

"I note with interest that during previous years' debate on the Greens' National Integrity Commission Bill 2016, Labor members of Parliament had outright opposed the establishment of an institution to to oversee the Commonwealth jurisdiction. However, during last month's debate, Labor senators appear to have shifted their positions."