Hundreds have died in Israeli attacks on southern Lebanon and the Gaza Strip, following abductions of Israeli servicemen by Lebanese and Palestinian militants.
At their meeting in Damascus, Bashar al-Assad and Alexander Saltanov "expressed their deep concern over the escalating conflict in Lebanon, and the deteriorating situation in the Palestinian territories," the ministry said.
The president and the Russian diplomat agreed the priority was to end the violence between Israel and Lebanon.
"The first step to ease tensions on the Lebanese-Israeli border must be a ceasefire, and then to address the causes of the crisis," the statement said.
Syria is a key player in the region and had troops in Lebanon for almost 30 years until they were pulled out after the assassination of former Lebanese premier Rafik Hariri. Israel and the United States have long suspected the Syrian leadership of supporting Hizbollah.
But the Syrian president said his country was willing to support the process toward securing a ceasefire by every available means.
Israel has carried out bombings and air strikes in Lebanon, and sent its troops into the country, in a wave of violence that began nine days ago when Islamic militant group Hezbollah captured two Israeli servicemen in a cross-border raid. Israel's attacks have left around 300 Lebanese dead and displaced 500,000, according to the Lebanese prime minister. At least 29 Israelis have also lost their lives.
Since the beginning of Israeli attacks in Gaza in June, when Palestinian militants abducted an Israeli corporal, the Israeli military has killed at least 110 Palestinians, around half of them militants.
The Russian Foreign Ministry said earlier that the armed conflict in Lebanon and the deteriorating situation in the Palestinian territories are undermining international efforts to regulate the Mideast conflict, and threaten to boost Islamic extremism around the world
"Such a turn of events not only puts under serious threat efforts by the international community to completely resolve the conflict in the region, but threatens an uncontrollable rise in extremist sentiment throughout the Islamic world," the ministry said in a statement.
The ministry also said that the scale of destruction caused in Lebanon and Palestine by the Israeli military has gone far beyond Israel's stated goals.
"Moscow confirms its commitment to a decisive war against terrorism in all its forms and manifestations. We also confirm our demands that that the captured Israeli servicemen be unconditionally freed. However, the unprecedented scale of fatalities and destruction shows that actions [on the part of Israel] to achieve this goal have gone far beyond the bounds of an anti-terrorist operation," the ministry's statement said.
