In the meeting that was held on Sunday, Dr Rouhani also said: "The Islamic Republic of Iran supported African nations, especially in South Africa, in their fight against Apartheid and today, we are very happy that there is acceptable security and stability in southern Africa".
He also expressed hope that terrorism be rooted out Africa, saying: "Terrorism is a dangerous disease that has created insecurity in some parts of Africa".
"One of our great responsibilities in today's world is establishing security and stability and combatting insecurity, instability and terrorism in countries across the globe," Dr Rouhani added.
He also emphasised respect and equal rights for all nations throughout the world, saying: "To realise this goal, political and international cooperation in international assemblies is very important and we believe that those countries that are seeking to dominate the world both in words and action, have chosen an incorrect path".
Tehran welcomes developing cooperation, said Rouhani, adding: "To develop cooperation, especially in economic fields, conditions and opportunities for investors of both countries need to be clear and easy".
At the same meeting, Prime Minister of Swaziland, Barnabas Sibusiso Dlamini also congratulated Dr Rouhani on his re-election and said: "Swaziland is on its path to advancement and we need to establish close ties with great countries such as Iran in this path".
"Swaziland attaches great weight to its relations and friendship with Iran and we are determined to deepen out ties in different fields of mutual interest," he said.
He also expressed his country's willingness to have close relationship with the Islamic Republic of Iran for peace and security.