"The agreements were not perfect but they do form a basis. We have to fulfil the agreements," Frank-Walter Steinmeier said at a meeting with Ukrainian Prime Minister Arseniy Yatsenyuk in Kiev.
"We hope that the tension will subside and Ukraine will regain its territorial integrity and sovereignty," Berlin's top diplomat said.
Yatsenyuk, however, lashed out at Kiev's former Soviet master by insisting that the September peace agreement "is being observed by Ukraine and blatantly violated by the Russian side."
"The restoration of control over the Ukrainian-Russian border, the stopping of weapons deliveries from the Russian Federation to Ukrainian territory, and the withdrawal of the Russian army and Russian terrorists from Ukrainian territory is not being carried out," he said.
Steinmeier was later due to fly to Moscow for a crunch sit-down with his Russian counterpart Sergei Lavrov.
On the ground, Ukraine's military said fresh clashes over the past 24 hours between government forces and rebels killed five of its soldiers despite a nominal truce that has halted fighting along much of the frontline but failed to stop bombardments at main flashpoints.
The European Union agreed to blacklist more Kremlin-backed rebels in Ukraine on Monday, but stopped short of fresh sanctions against Moscow, saying there was hope of restarting dialogue with Moscow to end the worst standoff since the Cold War.
New European Union diplomatic chief Federica Mogherini said foreign ministers meeting in Brussels had raised the possibility of her visiting Moscow to "re-engage in a dialogue" in search of a solution to the crisis that has claimed more than 4,100 lives.
The EU's defence ministers were also due to hold a meeting in Brussels on Tuesday to discuss the crisis, with NATO's secretary general Jens Stoltenberg attending the talks.
'Point of no return' not yet reached
Ahead of Steinmeier's visit, Russian Foreign Minister Lavrov said Moscow hoped "that the 'point of no return' has not yet been crossed" in its relations with Europe.
Lavrov cautioned there would not be a major breakthrough at the talks with his counterpart from Germany, which has been playing the lead role in mediating the crisis, but said Moscow wanted to reach "a balance acceptable to all parties."
The German foreign ministry said on Monday that the visit was aimed at assessing the "chances of avoiding a new spiral of violence in eastern Ukraine."
Lavrov's caution came as the tit-for-tat expulsions of a string of European diplomats have further heightened tensions between the 28-nation bloc and its vast eastern neighbour.
Moscow said it had expelled a German diplomat on Monday in retaliation for a diplomat being forced to leave Russia's consulate-general in Bonn, while several Polish diplomats were also expelled for alleged spying.
East-West relations already suffered a damaging blow when Russian President Vladimir Putin on Sunday left early from the G20 summit in Australia in the face of a stream of criticism from world leaders.
The EU has long been divided over sanctions. It initially limited them to individuals after Russia's annexation of Crimea in March, but then broadened them to target the Russian economy after the shooting down of Malaysian Airlines flight MH17 in July over eastern Ukraine.
The EU will add more separatists to the list of 119 individuals currently facing travel bans and asset freezes. Those previously targeted range from close Putin allies and Russian oligarchs to rebel leaders.
A final decision on the new names is due at the end of November.
Prepared for 'total war'
Ukraine has urged Brussels to go further to send a "clear message" to Moscow, after NATO said Russia had poured fresh armoured columns across the border last week.
Ukraine's President Petro Poroshenko on Monday wrote on Twitter that while Kiev wants to avoid all-out conflict, it is "prepared for a scenario of total war".
We are prepared for a scenario of total war.We dont want war,we want peace,we are fighting for EU values.Russia doesnt respect any agreement— Petro Poroshenko (@PoroshenkoEng) November 17, 2014
Russia rejects claims that it backs the rebels militarily but it openly supports them politically and it is unclear how the insurgents have acquired the heavy armour of a regular army.
Ukraine inked a string of agreements with the rebels in September on a ceasefire and rough roadmap for peace but the deals failed to get off the ground as fighting continued and the separatists held disputed elections.
Ukraine's military meanwhile said the rebels had shelled government positions 33 times over the past day, wounding eight servicemen in addition to the five killed.
The pro-Kiev governor in the war-ravaged Lugansk region, where separatists hold the main city, said a 43-year-old woman had her leg blown off by rebel shelling.