"President Barzani is a historic figure and courageous leader of his people, most recently in our common fight to destroy ISIS," State Department spokesperson Heather Nauert said in a statement. "This decision represents an act of statesmanship during a difficult period."
Barzani announced Sunday he would not participate in the Nov. 1 presidential elections.
"As a Peshmerga, I will continue at the service of our people; I refuse to get any extension and will not continue in this position; law should not be amended for me,” he wrote in a letter read aloud during the regional government's parliamentary session.
Nauert said the U.S. looked forward to engage with the new Prime Minister Nechirvan Barzani, as well as the Deputy Prime Minister, Qubad Talabani.
"A strong KRG within a unified and federal Iraq is essential to its long-term stability and to the enduring defeat of ISIS," the U.S. statement said, referring to the Islamic State of Iraq and Syria, another name for Daesh. "We call on all Kurdish parties to support the KRG as it works to resolve pending issues over the remainder of its term and prepare for elections in 2018."
On Sept. 25, Iraqis in KRG-controlled-held areas -- and in several disputed parts of the country -- voted overwhelmingly for independence from the Iraqi state.
The referendum had faced sharp opposition from most regional and international actors, who warned the poll would distract from Iraq’s fight against terrorism and further destabilize the region.
Violence between the KRG and Baghdad have erupted since the vote as tensions have risen between the two sides.
"We call on the Government of Iraq and the KRG under its new leadership to work urgently to resolve pending issues under the Iraqi constitution," Nauert said. "We have been encouraged by the security dialogue that has taken place in recent days, and call for an end to all confrontations and clashes."
Nauert also praised Iraqi Prime Minister Haider al-Abadi's decision to begin a new dialogue with the KRG and affirmed the U.S.'s support as he works to ensure the "total, and enduring" defeat of Daesh and a stable Iraq.
"We will continue to work with all parties as they address these issues for the benefit of all Iraqis," Nauert added. "It is time for all parties to look to the future and focus on peaceful resolution of disputes under the Iraqi constitution."