The ceremony, which took place at military airfield Severny, also included an honour guard procession by service members of all branches of the Russian Armed Forces - the Land Forces, the Air Force and the Navy.
President Kaczynski's coffin was placed on a stand in the centre of the airfield.
Vladimir Putin and Polish Ambassador to Russia Jerzy Bahr laid flowers at the coffin of Mr Kaczynski as the national anthems of both countries were played.
After the honour guard marched past, the coffin was loaded into a Polish Air Force plane. Prime Minister Putin, Ambassador Bahr, and the Polish and Russian delegations walked alongside the coffin as it was carried to the aircraft.