Trump specifically cited the Iran nuclear deal, which he wanted to pull the US out of against Tillerson's recommendations.
"We were not really thinking the same", Mr. Trump told reporters, according to The New York Times. In a surprise move, President Trump expressed a desire last week to meet personally with North Korean leader Kim Jong Un, with a meeting potentially happening within the next several months.
Additional reporting from Newsy affiliate CNN.
President Trump's axing of Secretary of State Rex Tillerson - delivered via Twitter for maximum humiliation - sends a clear message to everyone else in Trump's administration: If you don't fall in line with Trump, your time is running out.
It is highly unusual for a secretary of state to be replaced after only a year or so.
Tillerson had just returned from a shortened trip to Africa hours before Trump's announcement.
During his 14 months at the State Department, Tillerson had numerous policy differences with Trump - and the friction frequently played out in public. He has been criticized for defending the agency's use of torture.
Tillerson's sacking comes shortly after Trump, without consulting his top diplomat, made a decision to accept an invitation to talks with North Korea's Kim Jong-Un on resolving the Korean nuclear stand-off.
On Iran, Pompeo is expected to support Trump's desire to terminate the nuclear agreement crafted by the Obama administration-a break from Tillerson, who had warned ending the agreement would be extremely risky.
In December, Tillerson had offered to begin direct talks with North Korea without pre-conditions, backing away from a USA demand that Pyongyang must accept that any negotiations would be about giving up its nuclear arsenal.
Tillerson is only the latest of many high-profile officials to leave the White House. He also served on the National Security Council. Goldstein's swift firing after refuting the Trump administration's rhetoric further reinforces the erratic nature of the White House under Trump's tenure and stands as a cause for concern moving forward.
Trust that will prove vital in the coming weeks as the US has agreed to talks with diplomats and even the leader of North Korea.
Pompeo's military background suited him well at the Central Intelligence Agency, where he was a hard-liner on North Korea and the Iran nuclear deal.
The reports also said the techniques included slamming him against a wall, sleep deprivation and forced nudity.
Tillerson defended his record Tuesday, telling reporters that "working with allies, we exceeded the expectations of nearly everyone" with the "maximum pressure" campaign to denuclearize North Korea.
Goldstein was sacked later on Tuesday, two United States officials said. The accord was signed in 2015 by almost every country in the world, including the US and China.
"Tillerson's replacement by. Pompeo, who is known as a political partisan and an opponent of the Iran agreement, raises the prospect of the collapse of that deal, and increases the possibility that the administration might soon face not one, but two nuclear crises", he said. Despite his disagreements with Trump on policy, personnel, and leadership style, he remained committed to the role.