US Secretary of State Rex Tillerson is due to travel to Moscow this week and the spokeswoman for May said the two leaders had agreed during their conversation that the visit was an opportunity to make progress towards a solution.
On Friday, Johnson showed support for the USA airstrikes in Syria and called the Syrian chemical attacks "deplorable".
When asked about Washington's anti-Russia sanctions, the US Secretary of State said "there is no reason to be lifting sanctions".
In response, the U.S. says it destroyed a fifth of Syria's operational aircraft in an air strike on the Shayrat airbase last Thursday and said further strikes could take place.
U.S. President Donald Trump's strikes against the Syrian government earned the support of the American people and improved views of Trump (albeit only slightly), according to a new poll.
"I don't draw conclusions of complicity at all, but clearly they've been incompetent and perhaps they've just simply been out-maneuvered by the Syrians", Tillerson said in an interview with ABC's "This Week" program.
Both governments have defended their Damascus ally against Western allegations that it carried out a chemical weapons attack on the rebel-held town of Khan Sheikhun on Tuesday, killing dozens of civilians.
Two dead, two injured in shooting at California elementary school
The shooter is believed to be down, according to the Twitter account of San Bernardino Police Department Chief Jarrod Burguan . San Bernardino police and fire officials at North Park Elementary School on April 10, 2017 following shooting on campus.
US Secretary of State Rex Tillerson will press Russian Federation on its failure to prevent Syria's use of chemical weapons in meetings this week in Moscow, he said in interviews aired Sunday.
Saudi Arabia as well as Turkey welcomed the U.S. attack.
"It is time for (Russian president Vladimir) Putin to face the truth about the tyrant he is still propping up".
Elsewhere in Syria, US-led airstrikes killed at least 21 people, including a woman and her six children who were fleeing on a boat across the Euphrates River near the Islamic State group's self-styled capital, Raqqa, the target of a major offensive by US-backed and Kurdish-led Syrian forces, activists said.
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".
Foreign Secretary Boris Johnson pulled out of planned talks with Russian counterpart Sergey Lavrov after discussions with the United States, prompting claims he was Washington's poodle. And as our own Scott Clement noted Friday, actions like the one Trump took often gain more support after the fact.
A spokesperson for Russian Federation said only six Syrian Air Force MiG-23s, and a few buildings, were destroyed, with only 23 of the missiles reaching the Shayrat airbase.
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