Sixty-five people were killed when armed supporters of the Hezbollah-led opposition took control of much of Beirut after the US-backed government moved to outlaw the group's private communications network.
Ali Hamdan, spokesman for Nabih Berri, the parliament speaker, said that among the 200 dignitaries invited for Suleiman's election were also the foreign ministers of Syria and Iran.
Both countries are backers of Hezbollah.
Hamdan also said a US congressional delegation had been invited and would be headed by Nick Rahall, a West Virginia Democratic Representative of Lebanese origin.
"The speaker wants this election to be a reconciliation wedding," Hamdan said.
While the Doha accord brought the country back from the brink of civil war, it failed to address many key issues, including Hezbollah's weapons stockpile.
It also allows the opposition to have veto power on key policy decisions in a new cabinet of national unity.
Fouad Siniora, Lebanon's prime minister, said in an interview with the AFP news agency that he felt the deal was fair, especially in light of the latest violence that shook the country.
"We all gave in [for the sake of] the country and at the same time we got something in return for the country," he said.
"One has to look at the Doha accord as a package. It is a recognition by everybody who signed ... this agreement that weapons are in no way to be used against the Lebanese for political reasons."
Earlier in the week Suleiman told Lebanese media that it would be impossible to "save the country on my own".
"This mission requires the efforts of all. Security is not achieved by force but joint political will."
The presidency was left vacant in November, when pro-Syrian Emile Lahoud, who had also been the army chief, stepped down at the end of his term with no elected successor because of political disputes.
Though many see Suleiman as pro-Syrian in outlook, in nearly 10 years as head of Lebanon's armed forces, he has managed to avoid taking sides.
As the new head of state, he will need to show his is a neutral figure if he is to reconcile the interests of the Western-backed parliamentary majority and the opposition.