FILE PHOTO: Nationalist Movement Party (MHP) leader Devlet Bahceli addresses his supporters during a rally for the upcoming referendum, in Istanbul, Turkey, April 9, 2017.
Turks narrowly backed a constitutional change previous year to change the constitution and grant Erdogan sweeping powers.
The sides plan to discuss Bahceli's proposal to hold early presidential and parliamentary elections in Turkey, the Turkish media reported.
The eagerly-awaited meeting with Erdogan at his presidential palace lasted only half an hour, the presidency said.
Bahceli told MHP lawmakers that the elections - which are due to be held at the same time next year - should in fact be held on August 26, 2018.
Erdogan cited economic instability, the recent operation in northern Syria and a need "to overcome uncertainty" to bring forward polls from their planned November 2019 date.
Amy Schumer in talks for biopic on boxer Christy Martin
In the first teaser for the movie, Amy's character Renee gets a head injury that makes her see herself as lovely . I'm always happy when a film that I think is going to reinforce negative tropes really subverts them.
The early Saturday airstrikes hit three sites, one in Damascus, and two in the city of Homs, which US President Donald Trump claimed were "associated with the chemical weapon capabilities" of the Syrian government.
He precipitated the 2002 snap polls that brought AK Party to power.
Bahceli, who has led the MHP since 1997, used to be an outspoken critic of Erdogan but has closely aligned with the president since the July 2016 failed coup aimed at ousting him from power.
A day earlier, Rouhani said the USA -led airstrikes on Syria prove that Washington has direct ties with terrorists.
The main Turkey opposition party called for an end to it, insisting that a vote could not be held under emergency rule.
"The Americans showed such a reaction when they felt that the terrorists were dislodged from an important region like Eastern Ghouta", Rouhani said.