The U.S. strike on a Syrian air base came in response to the Assad regime chemical weapons attack on the town of Khan Shaykhun, Idlib province, killing some 100 civilians and wounding hundreds of others, mostly children.
"Developments in Syria have changed the situation fundamentally", Johnson said in a statement, according to a Reuters report.
Tillerson said he will raise the U.S.'s concerns with Foreign Minister Sergey Lavrov.
The hope, he said, is that "we can navigate a political outcome in which the Syrian people, in fact, will determine Bashar al-Assad's fate and his legitimacy".
Activists and state media said a separate airstrike by the US-led coalition on the ISIL-held village of Hneida killed at least 14 civilians, including children.
Following the suspected attack, US President Donald Trump launched air strikes against a Syrian government air base, and branded Syrian leader Bashar al-Assad a "dictator" who had "launched a disgusting chemical weapons attack on innocent civilians".More news: Malcolm Mitchell: 'Almost brought me to tears' to be mentioned by president
Mr Johnson told The Sun US president Donald Trump had shown "a resolve and willingness that has been sadly missing in the last few years" and warned the US could strike Syria again.
The Khan Sheikhun strike prompted Washington to take its first direct military action against Assad's government, with missile strikes against a central air base on Friday morning.
Syria has denied using any chemical agents, and Russian Federation says the U.S. gave no evidence Syria has chemical weapons.
Russian Federation meanwhile said a decision by the British foreign secretary to cancel a visit to Moscow later this month showed a lack of understanding of events in Syria.
Damascus and Moscow denied Syrian forces were behind the gas attack but Western countries dismissed their explanation that chemicals leaked from a rebel weapons depot after an air strike.
"If he needs to do more, he will do more", Haley said when asked if Trump would order more strikes.More news: EU urges Turkey to probe referendum vote
"What we have seen at the United Nations is a huge sigh of relief", Haley said.
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.
Russian Federation should end its support for "toxic" Syrian President Bashar al-Assad, British Foreign Secretary Boris Johnson said on Monday ahead of a meeting of G7 foreign ministers in Italy.
Russia's foreign ministry earlier condemned Johnson's decision not to come to Moscow, saying it showed that Britain had "no real influence on the course of global affairs".
Haley went on to say that the United States has the full support of the global community - both for its attack last week on a Syrian airstrip and for any future actions that may need to be taken.More news: United Kingdom parliament clears mid-term 'Brexit poll'
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