In a televised address, his first since Iraqi forces launched a surprise offensive to recapture Kurdish-held territory on October 16, Barzani confirmed that he would not extend his presidential term after November 1 "under any conditions".
The address followed a letter he sent to parliament in which he asked members to take measures to fill the resulting power vacuum.
Critics say the September 25 independence referendum, orchestrated by the 71-year-old president in the face of opposition from Baghdad and global allies, has weakened the position of Iraq's Kurds despite an overwhelming "yes" vote.
The Kurdish region was to have held presidential and parliamentary election on November 1 but they were postponed indefinitely last week amid the escalating regional crisis.
The central government retook the oil-rich city of Kirkuk, which the Kurds had held since 2014 and regard as both their spiritual homeland and a key source of revenue for their would-be independent state, in a military offensive on October 16. Iraqi government launched an offensive which led to Kurds losing to Baghdad large swathes of oilfields in the disputed province of Kirkuk. "We tried to stop bloodshed but the Iraqi forces and Popular Mobilization Front (Shi'ite militias) kept advancing, using USA weapons", he said.
Clashes broke out between the two sides after Iraqi forces captured the oil-rich city of Kirkuk from the Peshmerga, in a surprise offensive ordered by Abadi after the Kurds held an independence referendum in northern Iraq on September 25.More news: Davey Martinez is Nationals' pick for manager
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Barzani has led the KRG since it was established in 2005.
Turkey said the Kurdistan Region's move of freezing the referendum's results was not enough and will not fix what has been ruined.
The Elysee said in a statement that the two leaders "have already exchanged views several times" to seek for a diplomatic alternative to resolve the dispute between the Iraqi government and the Kurds who voted earlier this month for independence in a referendum that Baghdad said was illegal. In 2013 he refused to abandon the post, though his mandate expired. The two sides held a first round of talks on Friday and Saturday.
For his part, Prime Minister Haider al-Abadi's spokesman Saad al-Hadithi said on Saturday that the target of the Iraqi forces is to allow for its redeployment until reaching the Fishkhabur area on the Iraqi-Turkish border.
Abadi said the talks are meant to prepare for the peaceful deployment of Iraqi troops at the border crossings with Turkey, Iran and Syria in Iraq's Kurdistan region.
Abadi demanded on Thursday that the Kurds declare their referendum void, rejecting the KRG offer to suspend its independence push to resolve a crisis through talks.