Zelensky made the invitation during a telephone call with Steinmeier on Thursday, a source from the president's office told AFP, during which "past irritations were cleared up" and Steinmeier expressed his "solidarity, respect and support" for Ukraine.
A diplomatic spat had been rumbling between the two countries since Steinmeier admitted last month he had offered to visit Ukraine with other EU leaders, but this was "not wanted in Kyiv".
The German president, also a former foreign minister, has come under heavy criticism since Russia's invasion of Ukraine in February for his years-long detente policy towards Moscow.
Ukraine's ambassador to Germany in March boycotted a solidarity concert hosted by Steinmeier, protesting that the soloists featured on the programme were all Russians.
"In the middle of a war against civilians! An affront. Sorry I'm staying away," Andrij Melnyk wrote on Twitter.
Steinmeier and Scholz are both Social Democrats (SPD), who have over the years pushed for closer ties with Russia -- including energy ties that have left Germany heavily dependent on Russian gas.
Steinmeier admitted in April that he had made a "mistake" in pushing for Nord Stream 2, the controversial pipeline built to double Russian gas imports to Germany.
'Distorted and slanderous'
Criticism has also mounted against former chancellor and fellow SPD member Gerhard Schröder, who is a lobbyist for Russian gas and has a close friendship with Russian President Vladimir Putin.
Scholz, meanwhile, has been criticised for his own failure to visit Kyiv, as well as his hesitancy over providing heavy weapons to help Ukraine resist Russia's invasion.
Even as German opposition leader Friedrich Merz visited Ukraine this week, Scholz said he did not want to visit himself until Kyiv's differences with his fellow Social Democrat Steinmeier had been ironed out.
However, Germany did say last week it would send anti-aircraft tanks to Ukraine, in a clear switch in Berlin's cautious policy on military backing for Kyiv.
READ ALSO: Ukraine ambassador accuses Scholz of ‘throwing a strop’ over Kyiv trip
Scholz also expressed backing for a motion passed by the German parliament calling for the acceleration of the delivery of heavy weapons to Ukraine.
The chancellor has also hit back at criticism of the SPD, accusing his opponents of a "distorted and slanderous depiction" of its Russia policy.
In the telephone call on Thursday, Steinmeier said Germany "stands with united forces in solidarity at Ukraine's side", the source from the president's office said.
Both presidents described the talks as "very important and very good", the source said.
By Peter Wuetherich
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