The Muslim Brotherhood, the Wafd party, Tagammu, members of a committee chosen by youth groups, as well as independent political and business figures were present at the meeting.
The opposition groups were also represented by supporters of the National Coalition for Change led by Mohamed ElBaradei, without his presence, who was also active in the past 13 days of massive demonstrations.
Suleiman invited the opposition groups for talks last week, which was rejected by the groups.
Thousands of protesters still gathered in downtown Cairo's Tahrir Square on Sunday. But the order is under restoration, with banks resuming business, shops and schools reopening. Moreover, traffic went back to normal as more people started to use public transportation.
"These days the banks halted business. so I felt short of cash, " said Abbas, who queued up at a bank branch office in Cairo on Sunday morning.
A curfew which began on Jan. 28 in Cairo and two other governorates, is still in effect. Major tourist sites such as the Giza Pyramids remained closed.
U.S. Secretary of State Hillary Clinton said she supported the attendance of the Muslim Brotherhood, but would wait and see how the dialogue will develop.
The Brotherhood group refused to join talks with government earlier, saying that it decided to engage in negotiations to ensure the people's demands are met and to respect the sacrifices made by the young people.
"We decided to take part in a round of negotiations in order to test the official's seriousness about people's demands," said the group's supreme guide Mohamed Badie in a statement on Sunday.
The move to join negotiations after the Brotherhood rejected previous calls came only a day after the top executive board of the ruling National Democratic Party resigned en masse including Egyptian President's son Gamal Mubarak. Hossam Badrawi, a prominent physician and political figure was named as the new secretary general.