“These are difficult discussions we're having at the moment, and all my conversations with European colleagues show that we remain far from consensus and that a lot persuasion will still be necessary,” he said.
Steinmeier was speaking at a joint press conference in Berlin with his Italian counterpart Paolo Gentiloni, a day after European interior ministers failed to reach agreement on plans to tackle the Mediterranean migrant crisis.
The ministers took no decision to carry out European Commission proposals for quotas to redistribute 40,000 Syrian and Eritrean asylum-seekers who have arrived in Europe, and to resettle 20,000 Syrians living in camps outside Europe.
“Italy and Germany certainly both agree that we need to arrive at a more equitable distribution in Europe,” Steinmeier said.
“In our view, the best way is mandatory quotas for the European member states.”
More than 100,000 migrants have arrived in Europe this year, 60,000 through Italy alone, according to the EU's border agency Frontex.
Germany last year took in 200,000 asylum seekers and expects as many as 450,000 this year.
Steinmeier pointed to the role of Libya as a gateway for migrants and said “if we fail to stabilise … the rule of law in Libya, then it will be difficult to significantly reduce Libya's role as a transit country for refugees”.
EU leaders will hold fresh talks at a summit in Brussels on June 25-26.