Trump also repeated campaign-trail criticism of the Obama Administration for threatening military action and then backing off.
"Yesterday, chemical attack - a chemical attack that was so horrific in Syria against innocent people, including women, small children, and even beautiful little babies," Trump said during a Rose Garden news conference.
"Their deaths was an affront to humanity. These heinous actions by the Assad regime cannot be tolerated."
Haley led a special open session of the UN Security Council devoted to the chemical attack, which the US has blamed on the Assad regime.
The session was requested by France and Britain, but the attack in Idlib province poses a special challenge for the US, which holds the rotating presidency of the Security Council this month.
The Trump Administration has recently backed away from the long-standing view that the Syrian leader must leave office, saying in recent statements that its primary interest is combating Isis (Islamic State) in Syria, and that although Assad is an obstacle to peace, he is not the focus of US policy.
Russia's representative lamented what he called "clearly an ideological thrust" to the discussion at the Security Council.
Accusations of the Assad regime's involvement is "closely interwoven with the anti-Damascus campaign which hasn't yet reached the place it deserves on the landfill of history," Russian representative Sergey Kononuchenko said.
Syria's representative, Mounzer Moumzer, dismissed the accusation that his country was to blame, saying Damascus condemns the use of chemical weapons. "We don't have them. We never use them," he told the council.
Russian officials blamed Syrian rebels for the chemical attack that killed scores of people, many of them women and children, and that has been widely attributed to the Syrian Government.
The Russian claim - which rebel commanders and local activists denied - reflects attempts by Moscow to shield its ally after global condemnation for an attack that left victims gasping for breath and foaming at their mouths.
The World Health Organisation said that the symptoms bore all the hallmarks of a chemical attack, possibly involving a banned nerve agent. Syrian forces also have used chlorine-based weapons.
The UN ambassadors for Britain and France criticised Russia directly for protecting the Assad Government at the expense of civilians, and called on Russia to support a new UN resolution condemning the Syrian Government.
"History will judge all of us in how we respond to these unforgettable and unforgivable images of the innocent," British Ambassador Matthew Rycroft said. "How long are we going to sit here and pretend that actions in these chambers have no consequences?"
He said Russia and China squandered an opportunity to call out Syria when they vetoed a February effort to condemn smaller reported incidences of chemical weapons use.
The vetoes gave cover to Assad, Rycroft said, and the Syrian leader's response was to "humiliate" Russia with the attack this week. "This bears all the hallmarks of the Assad regime, and the use of chemical weapons is a war crime," he said.
French Ambassador Francois Delattre said the Security Council's credibility will be at stake if it again does not act, and he said Russia bears special responsibility as a sponsor of inconclusive peace talks between the Syrian government and rebel groups.
In the past, Syria's government and Russia have blamed Syrian rebel factions for attacks without offering any conclusive evidence.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, said that at least 72 people were killed, making it the deadliest chemical assault since 2013, when the Syrian Government dropped sarin on the Damascus suburbs, killing hundreds of people as they slept, and bringing the United States and Europe to the verge of military intervention.
Under Russian pressure, Syria agreed in 2013 to give up its chemical weapons and claimed it had eliminated its stockpiles.
