"We keep our hand extended toward the other party."
The Hezbollah-led opposition, supported by Syria and Iran, have agreed in principle with the ruling coalition to elect Suleiman.
However, a deal as to how power will be shared once Suleiman is elected has not been reached.
The presidency has been vacant since Emile Lahoud's term expired on November 23, precipitating the country's worst political crisis since the 1975-1990 civil war.
The rival camps had been at odds for weeks over who should be the new president before consensus emerged Suleiman, who was appointed army chief in 1998 when Syria controlled Lebanon.
Suleiman is known for his good relations with the Hezbollah, which is backed by Iran and Syria.
But the election has been held up by differences including the make-up of the new government and means to amend the constitution to allow a senior public servant to become president.