In an interview with Russian state television on March 29, Lavrov said the divisions between Moscow and the West on the Ukrainian crisis are “getting closer,” adding that recent contacts had shown the outlines of a "possible joint initiative which could be presented to our Ukrainian colleagues."
Ukraine's National Security Service chief Andriy Parubiy has said that some 100,000 Russian troops were massed on Ukraine's border. Western officials have cited far lower figures.
Lavrov said that Moscow's priority was to see Ukraine implement reform that would create a federalized structure, with every region having a degree of autonomy.
He also said Ukraine’s constitution should make clear that the country is a neutral state, ruling out NATO membership.
Later in the day, the Russian Foreign Ministry said Lavrov and U.S. Secretary of State John Kerry discussed the Ukrainian crisis as well as the timing of further contact. It said the telephone call was initiated by the United States.
Lavrov's comments come after similar reassurances from other Russian officials. UN chief Ban Ki-moon told reporters on March 28, after briefing the UN Security Council on his recent talks in Moscow and Kyiv, that Putin had reassured him there would be no invasion.
Ban also called on both Russia and Ukraine to engage in negotiations without further delay.
Russia's Ambassador to the UN Vitaly Churkin spoke immediately after Ban, accusing the Western members of the Security Council of trying to create a false impression of imminent Russian aggression.
"Our forces in Russia are undergoing their usual routine, staying in the barracks or doing some training. They are good forces, I must admit, but there is no worry of any Russian initiative against Ukraine," Churkin said.
On March 28, U.S. President Barack Obama urged Russia to pull back Russian troops from the border with Ukraine.
The White House said in a statement that Russian President Vladimir Putin called Obama on March 28, while the U.S. president was in Saudi Arabia -- the latest stop in a weeklong trip dominated by the Ukrainian crisis.
During the hour-long phone conversation, Obama urged Russia to offer a written response to a diplomatic proposal to the Ukraine crisis that the Washington has presented.
The proposal was developed after consultations with Ukraine and other European partners. It reportedly provides for the deployment of international monitors to protect the rights of Russian speakers in Crimea, and the return of Russian troops there to their bases.
Obama told Putin that Ukraine's government is pursuing deescalation despite Russia's incursion into Crimea, and urged Putin to avoid further provocations including the build-up of forces on its borders with Ukraine.
Separately, the Kremlin press service said in a statement that during their phone conversation, Putin drew Obama's attention to "the continuing rampage by extremists in Ukraine."