The 79-year-old Syrian diplomat had served as the nation's minister for foreign affairs since February 2006. Earlier in the day, the Syrian state news agency, SANA, reported that Muallem had passed away.
"With a deep sadness I learned about the death of my colleague Walid Muallem. Moscow will remember him as a wise diplomat who effectively worked out foreign policies entrusted to him during the country's difficult crisis years and who made a significant contribution to the development of bilateral Russian-Syrian relations," the Russian Foreign Ministry said, citing Lavrov's telegram.
The text of the telegram was transmitted through official channels to the Syrian side.
Earlier, Russian Deputy Foreign Minister Mikhail Bogdanov expressed his condolences over the death of Muallem and said that Moscow regrets losing this reliable partner.
"He was a highly experienced politician [...] We have lost a very reliable partner and sincere friend. I have always attached a great importance to our friendship," Bogdanov said.
Soon after the news of the death of the Syrian minister arrived, citizens of the Lebanese capital of Beirut, employees of diplomatic missions, ministers, the leadership of the country's ruling Arab Socialist Baath party and representatives of the Syrian intelligentsia took part in a farewell ceremony for Muallem at the Saad bin Maaz mosque in Damascus.
A number of senior officials, including those from China, Venezuela, Cuba, Palestine and Lebanon, have extended condolences over the death of Muallem.