Southern Lebanon was devastated after Israel launched attacks following the seizure of two Israeli troops in early July on the border with Lebanon by Lebanon-based radical group Hizbollah.
"Lebanon was mentioned as the issue of common concern since it is connected with the fight against terrorism," Alexander Kozlovsky, a deputy chairman of the State Duma Foreign Affairs Committee, said.
The G8 heads of parliaments met at the Tavrichesky Palace in St. Petersburg. In July St. Petersburg hosted a G8 summit as Russia holds this year a rotating chair in the organization.
He said the fight against new challenges and threats, particularly against terrorism, was one of the key issues on the meeting agenda.
Before the August 14 truce, Israeli military operations claimed the lives of about 1,000 Lebanese civilians, forced nearly a quarter of the country's population to flee, and demolished large parts of the country's infrastructure. About 160 Israelis were also killed in the fighting.
The UN deployed troops in southern Lebanon and has said it hopes to increase its contingent in the region to 15,000.