First appointed president in 2017, Social Democrat (SPD) Steinmeier, 65, last year said he would like to run again when Germany elects its next president on February 13th.
The Greens, who are part of a new three-way coalition government with the SPD and the liberal FDP, said in a statement they would be recommending that their MPs vote for him.
Steinmeier is a “very good and highly respected federal president who has rendered great service to our country during his first term”, they said.
The FDP has also said it will back Steinmeier.
The office of president is a symbolic role in Germany providing a counterpart to the head of government, currently Chancellor Olaf Scholz, also a Social Democrat.
One of Germany’s most popular and trusted politicians, Steinmeier was appointed as head of state after extended stints as foreign minister and chief of staff for former chancellor Gerhard Schroeder.
With his snowy white hair, round glasses and dimpled smile, Steinmeier is a trained lawyer with a reputation for being diplomatic and measured in his speech.
Announcing his desire to run for a second term last year, Steinmeier said being president had been an “honour” and an “enormous challenge”.
Presidents can run for a maximum of two terms in Germany, though Steinmeier would be only the fourth person to be re-elected to the role.