The veteran guerrilla leader has run Iraq's Kurdish autonomous region since 2005, presiding with a firm hand as the region prospered while the rest of Iraq struggled in civil war.
The decision comes just weeks after a referendum on independence, which was led by President Masoud Barzani.
He also informed parliament that he will not seek an extension of his term, which is set to expire November 1, but Barzani's senior assistant, Hemin Hawrami said the move did not mean the Kurdish leader was "stepping down".
He added that the presidential law of the region should not be amended nor should the term of the presidency be extended.
Barzani's request, which was approved by the regional parliament late Sunday, was to distribute his presidential powers among the Kurdish prime minister, the Kurdish parliament and the judiciary.
The televised speech marked a melancholic denouement for the Kurdish leader, weeks after he defied global and regional opposition to an independence poll held in Kurdish-majority provinces as well as in territories in dispute between Baghdad and Irbil, the capital of the Kurdish region.
Tehran had closed its borders with Iraq's Kurdistan region after it voted for independence in a referendum on September 25.More news: Iran asks United Nations nuclear chief to confirm it still follows deal
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The United Kingdom's Secretary of State for Foreign and Commonwealth Affairs on Monday urged Iraq and the Kurdistan Region to seek a quick and peaceful resolution to the current tensions.
Despite his resignation on Sunday, the former president - who has been at the forefront of Kurdish independence efforts for decades and the KRG president for 12 years - is expected to remain a senior political figure. Its borders with Turkey and Iran, the Kurds' top trading partners, were also seized. "We thought that the worldwide community would reward the peshmerga and the people of Kurdistan in return. We were a state within a state", said Kamal Chomani, a nonresident fellow at the Tahrir Institute for Middle East Policy, in a phone interview Sunday. Within weeks, a backlash from the vote revealed Barzani had miscalculated.
Local news outlets reported his supporters, many armed with sticks, broke into the parliament to insist that he remain in power. Opposition MPs who had been barricaded inside managed to leave later, according to their parties.
Barzani made the announcement on television Sunday.
Barzani's family continues to play an outsized role in the region's political hierarchy.
Abadi said he was following developments in the Kurdish area closely.