A joint command center made up of the forces of Russian, Iran and allied militia alliance supporting Syrian President Bashar Assad said the U.S. strike on a Syrian airbase crossed "red lines" and it would now respond to any new aggression and increase their level of support to their ally.

At the same time, U.S. Secretary of State Rex Tillerson blamed Russia's inaction for helping fuel a deadly poison gas attack against Syrian civilians last week, saying Moscow failed to carry out a 2013 agreement to secure and destroy chemical weapons in Syria.

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On Thursday, the U.S. bombed an Assad regime military base in response to the chemical weapons attack launched on Syrian citizens, in which 90 people including 30 children were killed.

According to a Pentagon spokesperson, 59 Tomahawk missiles were fired at Shayrat airbase outside of Homs, Syria, the site from which the U.S. suspects the chemical attack originated. Targets included "aircraft, hardened aircraft shelters, petroleum and logistical storage areas, ammunition supply bunkers, air defense systems and radars."

>> Read more: U.S. attack on Assad regime brings hope to rebels: 'First time Syrian children were not abandoned' >>

The overnight missile attack, which marked the first time the U.S. has directly targeted Syrian President Bashar Assad's forces, was condemned by his allies in Russia and Iran but welcomed by the Syrian opposition and its supporters, who expressed hope it signaled a turning point in the devastating six-year-old civil war.

In its statement, the joint command center of Assad's allies said: "What America waged in an aggression on Syria is a crossing of red lines. From now on we will respond with force to any aggressor or any breach of red lines from whoever it is and America knows our ability to respond well."

The statement said that the alliance, which includes the miitant group Hezbollah, will not be deterred from "liberating" Syria.

Also Sunday, Russian President Vladimir Putin and Iran's Hassan Rohani said in a phone call that aggressive U.S. actions against Syria were not permissible and violated international law, the Kremlin said.

The two leaders also called for an objective investigation into an incident involving chemical weapons in Syria's Idlib and said they were ready to deepen cooperation to fight terrorism, the Kremlin said in a statement on its website.

The Kremlin said the phone call took place on Iran's initiative.

On Saturday, the governor of Homs confirmed that the airbase was back in operation. "The airport is operating as a first phase," Homs governor Talal Barazi told Reuters. "Planes have taken off from it," he added, without saying when.

The statement by the joint command center on Sunday also condemned U.S. military presence in northern Syria as "illegal," saying its aim to control the area makes them "occupation" forces.

Almost 1,000 U.S. troops are in Syria as part of the ongoing preparation for the fight to oust the Islamic State group from its self-declared headquarters of Raqqa. Around 500 soldiers were deployed into Syria with heavy artillery guns, the U.S. said in March. According to the Pentagon, an additional "400 or so" Marines and Army Rangers have arrived early March.

The deployment is temporary, said Coalition spokesman U.S. Air Force Colonel John Dorrian, and the additional forces were sent to Manbij in the country's north in order to create "reassurance."

'Russia's failure'

Also Sunday, U.S. Secretary of State Rex Tillerson blamed Russia's inaction for helping fuel the chemical attack, saying Moscow failed to carry out a 2013 agreement to secure and destroy chemical weapons in Syria.

"I think the real failure here has been Russia's failure to live up to its commitments under the chemical weapons agreements that were entered into in 2013," Tillerson said on ABC's "This Week."

"The failure related to the recent strike and the recent terrible chemical weapons attack in large measure is a failure on Russia's part to achieve its commitment to the international community," he added.

Tillerson is expected in Moscow this week for talks with Russian officials.

He stopped short of accusing Russia of being directly involved in the planning or execution of the attack, saying he had not seen "any hard evidence" to suggest the nation was an accomplice to Syrian President Bashar Assad.

But he said the United States expected Russia to take a tougher stance against Syria by rethinking its alliance with Assad because "every time one of these horrific attacks occurs, it draws Russia closer into some level of responsibility."

Other than that, he added, "there is no change to our military posture" towards Syria.

Also Sunday, Ambassador to the United Nations Nikki Haley said in an interview that she sees regime change in Syria as one of the Trump administration's priorities. "We don't see a peaceful Syria with Assad in there," Haley said in an interview on CNN's "State of the Union" which will air in full on Sunday. The comments represented a departure from what Haley had said before the U.S. strike.

"You pick and choose your battles and when we're looking at this, it's about changing up priorities and our priority is no longer to sit there and focus on getting Assad out," Haley had told reporters on March 30, just days before dozens of Syrian civilians died from chemical weapons injuries.

Reuters contributed to this report