But his call was wrapped in kind words about the Syrian president and condemnation of the US strikes carried out on a Syrian airbase on Friday, in retaliation for a chemical attack on civilians in a rebel-held area of Syria.
In remarks from his Mar-a-Lago resort in West Palm Beach, Florida, President Donald Trump explained his decision to launch a military strike against a Syrian air base Thursday night, expressing disgust at the "very barbaric attack" by Syria.
For more of our interview with Secretary of State Rex Tillerson, tune in to "Face the Nation".
"Regime change is something that we think is going to happen because all of the parties are going to see that Assad is not the leader that needs to be taking place for Syria", she said.
After years of calling for Assad's removal during former president Barack Obama's tenure, Washington appeared to be stepping back from seeking regime change in Syria in recent weeks.
This week's airstrike "was a message to Bashar al-Assad that your multiple violations of your agreements at the United Nations, your agreements under the chemical weapons charter back in 2013, that those would not go without a response in the future", he said. Tillerson said during a trip to Turkey in late March that the "longer-term status of President Assad will be decided by the Syrian people".
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The government over the weekend backed away from the Supreme Court's ruling after strong global and domestic criticism. Tuesday's instability sent Venezuelan bonds lower, with the benchmark 2027 paper's price off 4.4 percent.
Moscow has been a steadfast ally of the Syrian government and has defended it against claims of chemical weapons use in front of the UN Security Council.
At least 87 people were killed - including women and children - in the assault on the Syrian town of Khan Shaykhun last Tuesday. "The failure related to the recent strike and the recent bad chemical weapons attack in large measure is a failure on Russia's part to achieve its commitment to the global community", he added.
Sadr became the first Iraqi political leader to call on Assad to resign even as he condemned the United States for the missile strikes on a Syrian airfield on Friday (7 April). It condemned the chemical attack, without naming Assad, calling instead for an global investigation to identify the perpetrator.
Tillerson is expected in Moscow this week for talks with Russian officials.
British Foreign Secretary Boris Johnson has cancelled a trip to Russian Federation over its support for Assad, prompting Moscow's foreign ministry to say London has "no real influence".
New strikes hit outside the town on Sunday, with no immediate reports of casualties, the monitor added.