Suleiman, who has headed the Egyptian intelligence service since the early 1990s, took up his mediating role in 2000, following the outbreak of the second intifada.
He had some success negotiating a brief ceasefire in June 2003.
But his critics have questioned his motivation - saying he is acting only to quell popular Egyptian sentiment.
Many also argue the temporary ceasefires simply allow Hamas and other Palestinian groups to rearm, often via smuggling tunnels running between Gaza and Egypt.
Suleiman was born in Qena, in the south of Egypt. He left for Cairo at the age of 19 to enroll in Egypt's military academy and went on to receive advanced military training in Russia.
He took part in in both the 1967 and 1973 Middle East wars, though details of his service are unclear
Both Mubarak and Suleimen survived an assassination attempt in Addis Ababa, the Ethiopian capital, where they were due to attend an African summit in June 1995.
The limousine Suleiman and Mubarak were travelling in came under fire, killing a number of bodyguards travelling with their convoy, before the driver was able to turn the car round and return to the airport.
The attack was blamed on members of the al-Qaeda-linked Egyptian Islamic Jihad, also known as the Society of Struggle, and said to be co-ordinated by Showqi al-Islambouli, a member of Egyptian Islamic Jihad.
His brother, Khalid Ahmed Showqi al-Islambouli, arranged and carried out the assassination of Mubarak's predecessor, Anwar Sadat, during a military parade in October 1981.
The Egyptian secret service regularly rounds up and arrests Muslim activists.