Mr Steinmeier is in the Ukrainian capital, Kiev, amid fresh attempts to find a diplomatic solution.
On Monday, pro-Russia activists in the east declared a separate state with a view to joining Russia, after holding votes on self-rule on Sunday.
Kiev, the US and EU say the referendums in Donetsk and Luhansk were illegal.
In Kiev, Mr Steinmeier met acting Ukrainian Prime Minister Arseniy Yatsenyuk and Foreign Minister Andriy Deshchytsya.
He said he hoped steps in Ukraine would "bring back occupied territory, disarm armed groups step by step, and reinstall the authority of the state".
In a separate development, Russian media quoted Luhansk separatists as saying that the self-declared governor of the region had been wounded in an assassination attempt.
Valery Bolotov was shot and had lost a lot of blood, but his life was not in danger, the press office of the self-declared "Luhansk People's Republic" said.
Later, the Russian foreign ministry said fresh EU sanctions would hinder efforts to defuse the crisis.
It urged the West to persuade Kiev to hold discussions on Ukraine's future structure and regional rights before the 25 May election.
The results of Sunday's referendums "should be a clear signal to Kiev of the depth of the crisis" in Ukraine, it said in a statement.
On Monday, the EU added 13 people and two businesses to its sanctions list for "undermining or threatening" Ukraine's sovereignty.
Meanwhile, the Kiev-appointed governor of Donetsk, Serhiy Taruta, said at a news conference in Donetsk that there were plans for a nationwide referendum on devolving more powers to the regions.
He said this could be held in mid-June and that members of the national parliament in Kiev might discuss it on Tuesday, reports the BBC's Richard Galpin in Donetsk.
Mr Taruta also said the self-declared "People's Republic of Donetsk" did not exist legally or politically, and that the Donetsk region could not survive economically as an independent territory.
Earlier, a separatist leader called on Russia to "absorb" the eastern Ukrainian region of Donetsk.
Armed separatists remain in control of many official buildings across eastern Ukraine.
Meanwhile, Russia's gas company, Gazprom, has asked Ukraine to pay $1.66bn (£1bn) for gas deliveries in June.
"Taking into an account non-working days, [Ukrainian gas company] Naftogaz should pay this bill by 2 June and, starting from 3 June, the company will be getting gas... only at the volumes paid for," Gazprom said in a statement.
Gazprom says Ukraine owes it $3.5bn.
It recently doubled the price Ukraine must pay for gas - a move that Kiev has refused to accept.
Moscow annexed Ukraine's southern autonomous republic of Crimea in March following a controversial referendum.
The Ukrainian government fears a similar outcome in Donetsk, Luhansk and parts of southern Ukraine.
Mr Steinmeier's trip is to support a national "round table" under the auspices of the Organisation for Security and Co-operation in Europe (OSCE).
The OSCE has issued a statement saying Russian President Vladimir Putin was "supportive" of its roadmap to defuse the crisis.
Germany, France and the UK have suggested that Russia would be further punished if it undermined Ukraine's planned presidential elections on 25 May.
Separatists in Donetsk and Luhansk say 89% and 96% respectively voted in favour of "self-rule" in the referendums.
NATO believes some 40,000 Russian troops are still deployed near Ukraine's border, although Moscow says they have been pulled back.
Source: BBC News Europe