The secularists, including powerful army generals, derailed an earlier attempt to have parliament elect Gul as president, a move that triggered early parliamentary elections which the AK Party won decisively last month.
A first round of voting in the presidential election will be held next Monday.
Secularists oppose Gul because of his Islamist past and the fact his wife wears the Muslim headscarf.
Gul, who denies any Islamist agenda, has already signalled he wants to run again. The cabinet debated the presidential election on Monday and talks continued late into the evening at the AK Party’s executive board.
Earlier, Mehmet Ali Sahin, the deputy prime minister, said ordinary Turks and AK Party officials favoured Gul’s candidacy, fuelling expectations that Tayyip Erdogan’s government will defy the army generals after its re-election.
The army, which views itself as ultimate guarantor of the secular order, ousted an Islamist-oriented government in which Gul served 10 years ago.
Gul is a gently spoken diplomat and an architect of Turkey’s European Union membership bid, but the secular establishment fears he would erode the separation of state and religion if elected, a claim he strongly rejects.
The leader of the secularist opposition Republican People’s Party (CHP) reiterated his objections to Gul’s candidacy, based on his role in the cabinet ousted by the army in 1997 and what he might mean for Turkey.
“Gul is a conscious member of an ideological circle,” Deniz Baykal told CNN Turk television.
“Turkey would become a country in which the political balances were changing very fast, in which the Middle East identity would become more pronounced.”