The United States is vowing to keep up the pressure on Syria after the intense night time wave of missile strikes from US ships, despite the prospect of escalating Russian ill will that could further inflame one of the world's most vexing conflicts.

Standing firm, the Trump administration on April 7 signaled new sanctions would soon follow the missile attack, and the Pentagon was even probing whether Russia itself was involved in the chemical weapons assault that compelled President Donald Trump to action.

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The attack against a Syrian air base was the first US assault against the government of President Bashar Assad.

Much of the international community rallied behind Trump's decision to fire the cruise missiles in reaction to this week's chemical weapons attack that killed dozens of men, women and children in Syria.

But a spokesman for Russian President Vladimir Putin warned that the strikes dealt “a significant blow” to relations between Moscow and Washington.

A key test of whether the relationship can be salvaged comes next week when Secretary of State Rex Tillerson becomes the first Trump Cabinet member to visit Russia.

Tillerson said he sees no reason for retaliation from Russia for the US missile strikes. Russia maintains a close political and military alliance with the Assad government and has been implicated in many of the attacks against Syrians opposed to Assad's rule, though Moscow adamantly denies such claims.

In an interview to air Sunday on CBS' “Face the Nation,” Tillerson said Russians were not targeted by the strikes. He also said the top US priority in the region hasn't changed and remained the defeat of Islamic State militants.

British Foreign Minister Boris Johnson also had planned to visit Russia this coming week, but decided on April 8 to cancel the trip because of the fast moving events in Syria. Johnson, who condemned Moscow's continued defense of Assad, said Tillerson will be able to give a “clear and coordinated message to the Russians.”

At the United Nations on April 7, Russia's deputy ambassador, Vladimir Safronkov, strongly criticised what he called the US “flagrant violation of international law and an act of aggression” whose “consequences for regional and international security could be extremely serious.”

He called the Assad government a main force against terrorism and said it deserved the presumption of innocence in the chemical weapons attack.

The US ambassador to the UN, Nikki Haley, said the world is waiting for the Russian government “to act responsibly in Syria” and “to reconsider its misplaced alliance with Bashar Assad.”