Iraqi prime minister Haider al-Abadi demanded the annulment of the vote and the transfer of border control and other infrastructure to federal forces.
Barzani also informed parliament that he will not seek an extension of his term which is set to expire November 1, Barzani's senior assistant, Hemin Hawrami said.
Critics say the September 25 independence referendum, orchestrated by the 71-year-old president in the face of opposition from Baghdad and worldwide allies, has weakened the position of Iraq's Kurds despite an overwhelming "yes" vote.
He told parliament he would remain as a member of the Peshmerga, the Kurdish fighting force alligned to the KRG and the Barzani family. Hawrami added that no political party submitted candidates to run against Barzani.
The UN Security Council called on the Iraqi government and Kurdish leaders not to resort to power and for ending escalation.
After reading the letter, parliament postponed their session for one hour to allow for further discussion.
Tensions have been running high between Baghdad and Erbil after the Kurds held a controversial referendum on the independence of the Kurdistan region and the disputed areas.
This led to a crisis with regional states opposed to the vote and the Iraqi government in Baghdad which launched a blockade on the Kurdish territories.
Within weeks, backlash from the referendum revealed it to have been an extraordinary miscalculation.
Meanwhile, following deadly clashes between Iraqi forces and Peshmerga forces, the global community seems anxious as there are efforts on several levels to defuse the crisis between Baghdad and Erbil. The region's airspace was closed to global commercial flights, Turkey threatened the use of military force and both Iran and Turkey threatened to close border crossings vital to the land-locked region.
Iraq's chief of staff General Othman al-Ghanimi told reporters after the talks in central Nineveh province that both sides have reached an agreement on some points.