"We actively encouraged... the Syrian leadership to make as concrete as possible its declared readiness for dialogue with the opposition," Lavrov told reporters after talks with his Egyptian counterpart Mohamed Kamel Amr in Moscow.
He said the Syrian government should stress its readiness for talks on the widest possible range of matters - in line with an international agreement in Geneva last June calling for a transitional government.
"I think a realistic and detailed assessment of the situation inside Syria will prompt reasonable opposition members to seek ways to start a political dialogue," added Lavrov, who last week said that neither side would win by force.
Russia expects to meet a senior US diplomat on Syria next month to discuss with international Syria envoy Lakhdar Brahimi his plans to end the civil war there, the Kremlin's envoy to the region said earlier on Friday.
Brahimi will visit Moscow on Saturday for talks on the results of his negotiations with Syrian President Bashar al-Assad and his opponents during a five-day trip to Damascus in which he called for political change to end the bloodshed.
Russia has also invited the head of the internationally-recognised, opposition Syrian National Council Moaz al-Khatib, to talks.