The two top diplomats discussed taking "concrete measures aimed at strengthening the ceasefire process in Syria" which was established in late February and has generally been holding, the foreign ministry statement said in a statement.
The measures would include steps to improve access to humanitarian aid and to fight against acts of terrorism in the country.
The telephone conversation between Lavrov and Kerry "took place on April 1 at the Americans' initiative," the statement added.
This issue calls for "agreement on the necessary actions as quickly as possible, including via the UN Security Council," the statement said.
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Russia has repeatedly accused Turkey of backing Islamist groups opposed to Syrian leader Bashar al-Assad, Moscow's ally in the five-year war.
The ceasefire reached in late February, led by Russia and the United States, is between the Assad regime and the rebels but does not include the jihadist groups Islamic State and the Al-Nusra Front.
Assad has said that any transitional government should include both the regime and opposition, without specifying which opposition groups should take part.