Lavrov, who spoke to reporters after meeting with Ukrainian Foreign Minister Andriy Deshchytsia in The Hague, where both attended an international security summit, said he outlined the steps that Moscow believes the new Ukrainian government has to make to defuse the crisis.
The meeting was the first encounter between the two ministers since last month's ouster of Ukraine's pro-Russian president and Russia's annexation of Crimea.
Lavrov, who also met with US Secretary of State John Kerry, said he reaffirmed Moscow's demand for a constitutional reform in Ukraine that would give more autonomy to all regions of Ukraine. Russia, eager to retain its influence in Ukraine's Russian-speaking eastern regions and prevent Ukraine from joining NATO, has pushed for Ukraine to become federation demands the new Ukrainian government has rejected.
Deshchytsia, who spoke to reporters before his meeting with Lavrov, said the Ukrainian government has remained concerned about a Russian military buildup near Ukraine's border.
Lavrov also said Moscow is unfazed by the West's intention to snub the Group of Eight summit that Russia was to host in Sochi in June.
Lavrov said the G-8 format has been useful in discussing global crises such as the Iran nuclear standoff or the Syrian civil war but said Russia "will not be clinging to this format." He added that Russia sees the broader Group of 20 nations as a more efficient format.