Russian and Iranian presidents in a phone conversation stressed the inadmissibility of "aggressive" US actions against Syria in violation of worldwide law, the Kremlin said in a statement issued on Sunday.
The strikes also prompted a backlash from Russian Federation.
Near the central city of Homs, a bomb exploded aboard a bus carrying workers, killing a woman and wounding more than 20, according to state TV and the Observatory.
The US responded to the poison gas attack, which is thought to have killed about 70 civilians, with a cruise missile strike on a Syrian regime air base on Friday.
During the meeting, Haley openly questioned Russia's role in Syria and said Russian Federation was supposed to be responsible for removing chemical weapons from Syria.
McMaster told Fox News Sunday host Chris Wallace the "president acted decisively" and that while the strike wasn't meant to take out all of Syria's capabilities, "it was a strong signal that the USA will not stand idly by".
But the Russians are denying that Assad had anything to do with the chemical attack.
Medical workers and experts say victims of the the chemical release displayed symptoms consistent with a potent nerve agent, possibly Sarin. Instead, he was thrust to the forefront after photos of the bodies piled in heaps in Idlib, Syria, dramatically altered the agenda.
"If Russia wants to be absolved of responsibility for future attacks, (President) Vladimir Putin needs to enforce commitments, dismantle Assad's chemical weapons arsenal for good and get fully engaged" with the United Nations peace process on Syria.
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The US says the base was used in the Syrian attack in Khan Sheikhun in rebel-held Idlib province, whose victims included 27 children.
British Defence Secretary Michael Fallon criticised Russia's support of Assad, describing the chemical attack as a war crime that happened "on their watch".
He had planned to travel to Russia Monday on a trip meant to start a fresh dialogue with Moscow.
US Secretary of State Rex Tillerson blames Russia's inaction for helping fuel a deadly poison attack against Syrian civilians last week.
"I think what we should do is ask Russia, 'How could it be if you have advisers at that airfield, that you didn't know?"' Mr McMaster said.
In one interview, Tillerson said he sees no reason for retaliation from Russian Federation for the US missile strikes. To the American people, the war never ends with Assad.
In a separate development, activists opposed to the Islamic State group said a USA -led coalition airstrike hit a boat carrying civilians fleeing across the Euphrates River. He also said the top USA priority in the region hadn't changed and remained the defeat of ISIS.
In February the North simultaneously fired four ballistic missiles off its east coast, three of which fell provocatively close to Japan, in what it said was a drill for an attack on United States bases in the neighbouring Asian country.
Haley disagreed, telling Tapper that the USA government has evidence. The Observatory said 15 people, including four children, were killed in the airstrike.
Graham said he supports the president's decision to order the strikes, but wants to see more from the administration on Syria.