The Kremlin says Russian President Vladimir Putin told his Ukrainian counterpart, Petro Poroshenko, on September 9 that Moscow remained committed to "further assist" the Ukraine peace process.
The Kremlin said in a statement that in the course of the telephone conversation, "the importance of maintaining a steady a cease-fire regime in the southeast of Ukraine was stressed."
The cease-fire, which took effect on September 5, appears generally to be holding, despite violations reported by both sides.
Earlier, Russian Foreign Minister Sergei Lavrov said he hoped that talks would start soon on the status of eastern Ukraine, where pro-Russian separatists have been waging an armed rebellion.
Lavrov also claimed there was a "heavy concentration" of government forces in an area northeast of Donetsk and accused Kyiv of preparing a strike against the rebels despite a cease-fire.
The separatists are seeking independence for the eastern Donetsk and Luhansk regions, where they declared so-called "people's republics."
The Ukrainian government has promised greater autonomy to the mainly Russian-speaking region but rules out independence.
From RFE/RL'S Brussels correspondent Rikard Jozwiak:
It is a very messy situation.
Officially, Finland has taken the blame for stopping the new sanctions from taking effect for now. Their prime minister last night said that they are supporting the sanctions but that they need more time to implement them.
But there are more countries in that camp, including Slovakia, Hungary, Austria, Italy, Bulgaria, and Cyprus. They are all happy for this to just to go away. The more "hardcore" countries are obviously not too happy with this but both the Swedish and Lithuanian diplomats I spoke to seem to concede that there has been some improvement in Russian-Ukrainian relations in the last 48 hours to warrant a more cautious approach.
They are also pointing to the fact that there was a sort of compromise on September 8 because the statement by Herman Van Rompuy says that the measures will enter into force with the publication in the EU's official journal in the next few days.
But as I understand it, the sanctions might very well be published but also annulled at the same time so they never properly enter into force. The key sentence of the statement reads: "Depending on the situation on the ground, the EU stands ready to review the agreed sanctions in whole or in part."
Already on September 10 at 11.00 ambassadors will meet again to assess the implementation of the cease-fire and the peace plan. If there is no deterioration, the sanctions might very well never enter into force.
A 12-point protocol signed at talks in the Belarusian capital, Minsk, on September 5 called for the decentralization of power but did not specify what special status the regions of Donetsk and Luhansk should have.
It also called for an "inclusive national dialogue."
The talks in Minsk involved representatives of Ukraine and the separatists, as well as envoys from Russia and the Organization for Security and Cooperation in Europe.
The cease-fire, which took effect on September 5, appears largely to hold, despite violations reported by both sides.
Ukrainian military spokesman Andriy Lysenko said on September 9 that five Ukrainian servicemen have been killed during the cease-fire.
Lysenko also said the separatists have so far released 648 prisoners to the government side under the agreement.
The European Union on September 8 formally adopted new economic sanctions against Russia over its role in Ukraine but delayed their enforcement to allow time to determine whether the cease-fire can take hold in eastern Ukraine.
A European Commission spokeswoman, Pia Ahrenkilde, said on September the sanctions will enter into force "in the next few days."
The EU has said the sanctions could be suspended if Moscow honors the conditions of the cease-fire and pulls its troops out of Ukrainian territory.
Russia denies sending troops and weapons across the border to support the separatists.
EU diplomats said that the new sanctions included a ban on loans and financing from EU countries to major Russian energy firms -- including Rosneft, Transneft, and Gazprom Neft.
Russian Prime Minister Dmitry Medvedev told the Russian daily newspaper "Vedomosti" on September 8 that Western airlines could be banned from Russian airspace "if there are sanctions related to the energy sector, or further restrictions on Russia's financial sector.”
Meanwhile, the U.S. State Department said on September 9 the United States is putting the finishing touches on possible new sanctions on Russia's defense, energy, and financial sectors over Ukraine.
State Department spokeswoman Marie Harf said at her daily briefing, "We have tools at the ready. We are finalizing these packages, but we are going to make decisions based on what's happening on the ground in the next few days."
With reporting by Reuters, AP, AFP, and "Interfax"