Germany and Spain condemned Friday's deadly suspected Islamist attack on a gas factory in their neighbour France, branding it "heinous" and vowing to stay united against "barbarism".
"We extend our deepest sympathies to the victims' families and see ourselves as united with France in defence of our free society against terror's blind hate," Steinmeier said in a statement.
The foreign minister said he was appalled by the "shocking news of a heinous murder and an assault with several injured".
He called it an "act of terror and fanaticism which we condemn in the strongest terms".
Meanwhile, Peter Altmaier, the head of Chancellor Angela Merkel's office, tweeted in French that the attack "recalls once again European common values," and offered "all solidarity and our condolences".
L'attentat affreux en Isere nous rappel une fois encore les valeurs communes de l'Europe! Toute la solidarite et nos condoleances— Peter Altmaier (@peteraltmaier) June 26, 2015
An Interior Ministry spokesman said that investigators from Germany's Federal Police (Bundeskriminalamt) were already in "close co-operation" with their colleagues in France, the Saarbrücker Zeitung reported.
"I firmly condemn the attack carried out in Lyon. Barbarism will always be confronted by unity among democrats. #Spain with #France," Spanish Prime Minister Mariano Rajoy wrote in a message on Twitter.
A severed head was pinned to the gate of the factory near Lyon in southwestern France during what French President Francois Hollande described as a "terrorist attack".
Several other people were also injured in the attack, in which a suspect set off several small explosive devices, sources close to the investigation said.
The suspect arrested in connection with the attack was investigated nine years ago for radicalization and has links to the Salafist movement, Interior Minister Bernard Cazeneuve said later.
The killing came nearly six months after the Islamist attacks in and around Paris that killed 17 people in January, starting with a shooting at satirical magazine Charlie Hebdo.