In an earlier statement released to the media, State Department spokesman Steve Goldstein said Tillerson "had every intention of staying because of the critical progress made in national security", particularly on the latest opening with North Korea.
Goldstein was sacked later on Tuesday, two US officials told Reuters.
One of the disagreements is over the Iran deal, which Mr Trump has said is awful. I wanted to either break it or do something and he felt a little bit differently.
The official said Trump works well with Pompeo, a former Republican congressman from Kansas, and wanted him in place before the US president's planned talks with North Korean leader, Kim Jong Un, and trade negotiations.
No one elected Tillerson to make these decisions.
"She may face the same tough choice that Tillerson and others have faced: Stick to your convictions or knuckle under to keep your job", a fourth official said.
Trump also thanked Tillerson for his service. He also laced his remarks with what could be seen as personal digs at the president.
But the State Department plays a direct and key role in climate change - not just in worldwide climate negotiations, but also in global aid and development, including choices about which energy sources developing countries should choose - so, such non-answers given as by Pompeo previously should not fly this time around. He also urged them to confront "challenges of sexual harassment within the department".
The official was responding to a question on the timing of Trumps announcement.
Perhaps Trump's most consequential firing came last May, when he dismissed FBI Director James Comey. Comey did not know whether he was authorized to take the FBI plane back home to Washington, D.C. The FBI sent him home without waiting for authorization.
"I have been told that Tillerson was getting increasingly angry over the Trump crackdown on China", Michael Pillsbury, a senior fellow at the Hudson Institute and China policy expert who served as an adviser to various presidential administrations, told FOX Business.
Trump said Tuesday that he might condemn Russian Federation for the attack but would have to talk first with the British prime minister. "We got along actually quite well but we disagreed on things". He added that, "If he's confirmed, we hope that Mr. Pompeo will turn over a new leaf and will start toughening up our policies towards Russian Federation and Putin".
Sen. Dianne Feinstein (D., Calif.) on Tuesday said that Gina Haspel has been a "good deputy director of the Central Intelligence Agency", but said that she would wait until the confirmation hearing to determine whether she will vote for Haspel to be the next director of the Central Intelligence Agency.More news: Michael Carrick Announces Retirement From Football
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Pompeo's nomination was expected to go smoothly, but Haspel's could be problematic.
Haspel, who has spent much of her career in covert action, allegedly ran a "black site" in Thailand that used harsh interrogation techniques and has been charged by human rights groups with attempting to destroy evidence of the interrogations.
In a statement, Sen.
He has opposed same-sex marriage, winning him criticism from the gay community, and on Tuesday the Council on American-Islamic Relations accused him of expressing anti-Muslim views and urged the Senate to reject his nomination.
Trump appointed Gina Haspel as the new CIA Director, terming her elevation as "a historic milestone".
While he espoused unconventional views on the organization of the State Department - and made sweeping reform of the bureaucracy his top concern - Tillerson proved to be cut from the same cloth of the national security conservatives who have dominated the GOP for decades. He said his formal resignation would officially take place at midnight March 31.
Tillerson and his cabinet ally Defense Secretary Jim Mattis have urged Trump to listen to his European allies and to preserve the deal intact, while seeking new measures to pressure Iran.
America's interlocutors, Haass added, will now believe the secretary of state "is speaking with the power and backing of the President".
Their differences were apparent nearly from the start.
Tillerson's insult to Trump's intelligence came after heated discussions about Afghanistan policy, in which Trump had pushed to end the US presence altogether and flirted with outsourcing the military counterterrorism campaign to private contractors.
"I'm not sure how strong a force Tillerson was on the question of the Iran deal so the underlying assumption that Tillerson is keeping Trump in the Iran deal, I'm not sure that's the real story", Murphy told Al-Monitor.
Then yesterday the axe fell on Tillerson himself.
Tillerson later denied that he was considering resigning but did not specifically deny calling Trump a "moron".