"Sri Lanka and Iran enjoy strong historical bilateral ties that predate the modern diplomatic relations which were established more than six decades ago," Rajapaksa said.
He said he is looking forward to working with President Rouhani to further strengthen the bilateral ties, according to officials.
Rajapaksa and Rouhani's predecessor Mahmoud Ahmadinejad had become close allies.
Ahmadinejad visited Sri Lanka in 2008.
Iran extended bilateral assistance to the island nation, including a pledge to modernise the country's only refinery.