Peres, visiting Moscow, met with the Russian president, RIA Novosti reported.
"The border with Syria has been silent for many years, and we would like it to stay that way," Peres said afterward. "I believe Russia and you have an important role: You can stop the bloodshed in Syria and bring peace and security not only to Syria but also to the Middle East."
Russia and China oppose intervention to help the Syrian rebels, saying they and Syrian President Bashar Assad are to blame for violence there. Both have used their vetoes on the U.N. Security Council to block sanctions against the Syrian government.
Thousands of people have been killed in Syria since large demonstrations began last year, and the country is now in a civil war.
Peres also warned Russia: "Those who deny the possibility of a disaster in Iran may indirectly cause it."