Speaking to journalists after talks with Latvian Foreign Minister Edgars Rinkevics, Steinmeier said supplying arms to Ukraine could lead to a situation of creating "victims on top of victims."
"We believe we must make another effort to try to end the violence," Steinmeier said.
"Our position is that the current situation would not be helped by us providing arms."
Rinkevics offered a slightly different line ahead of a meeting of EU leaders on February 9 which is due to decide what extra action the bloc will take as Russian-backed forces seize more territory in eastern Ukraine.
"The European Union does not think that supplying arms would help the de-escalation of the situation in Ukraine, but it is up to the individual states to decide their own position... I do not want to criticise member states that do take that position," Rinkevics said.
He also voiced hopes that with the Minsk peace agreements seemingly in tatters, the so-called 'Normandy Format' of talks between Russia and Ukraine, alongside France and Germany, might offer some hope for a negotiated settlement.
"I hope that the Normandy Format will continue, to search for a solution and help the situation in Eastern Ukraine to normalize," Rinkevics said.
Countries including Latvia's neighbors Lithuania and Estonia have backed the idea of sending arms to Ukraine in principle to help government forces counter huge amounts of arms provided to rebels by Russia.
However, lacking the sorts of arms required themselves, the Baltic states are mulling other forms of support, which Rinkevics said could take the form of logistics or help in reforming the Ukrainian military.