Tillerson spoke after a meeting of the "likeminded" countries was hastily arranged on the sidelines of the summit of the Group of Seven industrialized economies in Italy. US President Donald Trump will attend North Atlantic Treaty Organisation and G7 leaders' summits in late May - in effect, the diplomatic can has been kicked down the road until then.
Haley said that the Trump administration's view was that a political solution would not happen with Assad in power, though she stopped short of saying Assad's departure was now official USA policy.
Spicer says at his daily press briefing that "there is no question that" Ivanka Trump and others "weighed into him" on the decision.
Reuters reports that Putin's spokesman, Dmitry Peskov, says that "right now there is no meeting with Tillerson in the president's diary".
"Right now, I think everyone in the world sees Russian Federation as part of the problem", McMaster said.
The strikes hit the government's Shayrat air base in central Syria, where US officials believe the planes that carried out the Syrian chemical attack left from, the AP reported.
The decision to not receive Tillerson could raise tensions between the US and Russian Federation following the American airstike on Syria.
In a gesture weighted with symbolism, Tillerson visited the site of a World War II-era Nazi massacre in central Italy on Monday.
It feels very long ago, but after the September 11, 2001, attacks, Russian President Vladimir Putin was the first foreign leader to call Bush, and Russia sent military medical teams as part of the USA -led coalition against al-Qaida and the Taliban in Afghanistan.
The April 4 chemical weapons attack on the rebel-held town in Idlib province left almost 90 people dead. "The more complicated subjects will be left to the leaders", said an Italian diplomat, who declined to be named because he was not authorized to speak to the press.
Tillerson is traveling Tuesday to Moscow. The Kremlin wants to know if the strike was a one-time intervention or if it signals a deeper involvement by Washington.
Until the chemical attack, Trump had said Washington would no longer act as the world's guardian, especially if it was not in the interests of the United States. But he said Trump now needed to work with Congress to set a future course.
US Secretary of State Rex Tillerson issued an ultimatum to Russian Federation on Tuesday: Side with the US and likeminded countries on Syria, or embrace Iran, militant group Hezbollah and embattled Syrian leader Bashar Assad.
Haley added that USA intelligence showed there was no doubt the Syrian regime was behind the chemical attack.
Sen. Ben Cardin of Maryland, the top Democrat on the Foreign Relations Committee, agreed. He says the USA can't get involved in Syria's civil war, but couldn't allow the use of chemical weapons.
"We have seen it all already", Putin said.
Still, Sen. Lindsey Graham, R-S.C., said he believed that Trump didn't need to consult with Congress.
Mattis criticized Assad for using chemical weapons several times over the last several years.
Putin blamed the USA for aiding revolutions that toppled pro-Russian leaders in Ukraine and Georgia, and he blamed Hillary Clinton for inspiring Russian protesters when Putin was running for president in 2012.
Instead, the plan was shelved until after the results of an investigation into the attack on the rebel-held town of Khan Sheikhoun last week, which prompted the U.S. to launch a barrage of missiles on a Syrian airbase on Friday.
The missile attack has increased expectations that Trump is ready to adopt a tougher stance with respect to Russian Federation, and that he is ready to engage in world affairs, instead of following the more isolationist stance he had previously taken.
Russia's defence ministry also said it had information that rebel fighters were bringing "poisonous substances" to the areas around the Syrian town of Khan Sheikhun and Eastern Ghuta, among other places.
The White House official slammed Russian Federation for siding with the Assad regime that has used chemical weapons against its own people.
Just 18 percent approve of USA ground troops in Syria.
He said Russian Federation had a choice: to continue backing the "toxic" Assad regime, "or to work with the rest of the world to find a solution for Syria, a political solution".
Also on Monday, Britain and Canada said sanctions could be tightened on Moscow if it continues to back Assad.