Defeating the Islamic State in Iraq and Syria (ISIS), pushing Iranian influence out of Syria and the ouster of Syrian President Bashar al-Assad are priorities for Washington, Ms Haley said in an interview on CNN's "State of the Union".
That attack followed a chemical attack on the northern town of Khan Sheikhoun that killed 87 people.
The conversation was initiated by the American side, the statement said. Just days prior, the regime used the airbase to launch a chemical weapons attack on a nearby rebel-held city.
Tillerson said he has "not seen any hard evidence" that Russians were involved in planning or carrying out the attack.
"It is clear that Donald Trump does not have a clear or comprehensive strategy to hold Assad and his enablers in Russian Federation accountable", he said.
Tillerson says the Islamic State group is a threat not just to the US but to stability in the region.
The White House is circulating a letter President Donald Trump sent to the leaders of both houses of Congress explaining his decision to order military strikes on a Syrian air field.
Elsewhere in Syria, US-led air strikes killed at least 21 people, including a woman and her six children who were fleeing on a boat across the Euphrates River near ISIL's stronghold, Raqqa.
President Donald Trump ordered the strike in response to a chemical weapons attack against civilians earlier in the week, which U.S. officials say was carried out by the Assad government.
Russian Foreign Minister Sergei Lavrov told US Secretary of State Rex Tillerson in a phone call that an attack on Syria plays in the hands of extremists, Russia's Foreign Ministry said on Saturday after the phone call from Tillerson. He also said the top USA priority in the region hasn't changed and remained the defeat of Islamic State militants.
Russian Prime Minister Dmitry Medvedev said the strikes had left the USA "on the verge of military clashes with Russia".
"I feel that was accomplished", she said.
And thought some Democrats have criticized her hawkishness toward Syria and Assad in the past, she also mentioned Trump's policy, saying, "We can not speak in one breath of protecting Syrian babies and in the next close American doors to them".
The president also mentioned Turkish government statements saying that the use of a nerve agent was detected during the treatment of chemical weapons attack victims on the Turkey-Syria border in the presence of World Health Organization (WHO) experts.