The U.S. on Monday emphasized the importance of maintaining Iraq's territorial integrity as the country's Kurdish Regional Government (KRG) votes in a non-binding referendum on their future with Iraq.

"We hope for a unified Iraq to annihilate [Daesh] and certainly a unified Iraq to push back on Iran," White House spokeswoman Sarah Huckabee-Sanders told reporters.

The U.S., along with Turkey, the U.K., Iran and the Iraqi central government have urged Irbil to abandon the controversial poll but the vote went ahead Monday unhindered.

Iraqis in areas held by the KRG and in a handful of territories disputed between Irbil and Baghdad — voted to decide whether to secede from Iraq.

Earlier Monday, Turkish President Recep Tayyip Erdoğan said Turkey would take political, economic, commercial and security steps against the Kurdish Regional Government.

Iraq's central government has threatened to intervene militarily if the vote leads to violence.

KRG leader Masoud Barzani, however, said a "Yes" vote would not result in an automatic declaration of independence but would simply lead to further negotiations with Baghdad.

The State Department said last week the referendum would preclude the possibility of negotiations with the Baghdad central government, and present a high cost for "all Iraqis, including Kurds."

It cited disruptions in the fight against Daesh, which the KRG's peshmerga forces support, as well as worsening trade relations with neighbors and the destabilizing nature of holding the referendum in internationally disputed areas.

In contrast, "genuine dialogue" promises to resolve Iraqi Kurds' grievances and establish a new course in Baghdad-Irbil relations, the department said at the time.

Meanwhile, Huckabee-Sanders also said that the U.S. was not seeking to overthrow North Korea's government after the president tweeted that Kim Jong Un "won't be around much longer" and called Pyongyang's assertion absurd that Donald Trump's comment amounted to a declaration of war.

At the U.N. on Monday, the North's top diplomat, Ri Yong Ho, argued that Trump's Twitter blast gives it the right to shoot down U.S. warplanes, like the strategic bombers Washington flew close to the border between the two Koreas over the weekend.

Trump's Saturday tweet said: "Just heard Foreign Minister of North Korea speak at U.N. If he echoes thoughts of Little Rocket Man, they won't be around much longer!" Trump also used "rocket man" for Kim in his speech to the U.N. General Assembly last week.

While the comments may be read as an implicit threat to eliminate Kim, administration officials said Washington hadn't changed its policy and the U.S. isn't seeking regime change in Pyongyang.

"We have not declared war on North Korea. Frankly the suggestion of that is absurd," White House spokeswoman Sarah Huckabee Sanders told reporters. "It's never appropriate for a country to shoot down another country's aircraft when it's over international waters."

"Our goal is still the same. We continue to seek the peaceful denuclearization of the Korean Peninsula," she said.