"I think as time goes on, every day that has passed, he more and more has understood the gravity of USA leadership", said GOP Sen.
The move immediately prompted a backlash from Russian President Vladimir Putin, who said it would damage US-Russian relations. The Observatory said 15 people, including four children, were killed in the airstrike.
Dictator Bashar al-Assad has repeatedly attacked his own people over the past six years of that three-sided civil war.
The U.S. Congress is divided over Thursday's missile strike at Syria ordered by President Donald Trump, with some lawmakers voicing strong support while others questioning its constitutionality.
The heads of the general staffs of Iran and Russian Federation, a close ally of Assad, spoke by telephone on Saturday and condemned the USA strikes as "blatant aggression. aimed at slowing a trend of victories by Syria's army and its allies and boosting the terrorists' morale", Iran's state news agency IRNA said.
He said: "The greatest war criminal of all, Bashar Assad, has now been put on notice".
In Damascus, dozens of Syrian students gathered outside the offices of the United Nations to protest against the USA missile attack.
"The reality of today shows that we must stand against power with power and it proves a million times over that our decision to strengthen our nuclear deterrence has been the right choice". There were some steps taken to that effect such as the meeting with the chiefs of staffs, and de facto cooperation in the north of Syria.
The comments from Tillerson and Haley suggested that the airstrikes Trump ordered punishing Assad for using chemical weapons would not lead to any immediate change in USA strategy toward Syria.
Russian prime minister Dmitry Medvedev said the strike had brought Moscow and Washington to the verge of a "military clash", adding that the action was "good news for terrorists".
However, most mainstream conservatives endorsed Mr Trump's order to fire 59 Tomahawk missiles at a Syrian military air base to punish and warn the Assad regime.
It followed days of outrage over images of dead children and victims suffering convulsions from the suspected sarin gas attack in the rebel-held town of Khan Sheikhun.
It was Trump's biggest foreign policy decision since taking office in January and the kind of direct intervention in Syria's six-year-old civil war his predecessor Barack Obama avoided.
Trump was meeting again with his Chinese counterpart Friday, with USA missile strikes on Syria adding weight to his threat to act unilaterally against the nuclear weapons program of China's ally, North Korea.
Donald Trump spoke by telephone with Saudi Arabia's King Salman about the strikes, the Saudi Press Agency said on Saturday. While Trump's action has won praise across the globe, it has drawn protest from Russian Federation and Iran, Assad's only allies. At the U.N. Security Council, U.S. Ambassador Nikki Haley mocked Moscow for failing to rid Syria of chemical weapons under a 2013 deal.
Russia, one of the main backers of the Assad regime alongside Iran, condemned the USA strike, denouncing a "flagrant violation of worldwide law and an act of aggression".
It comes as President Trump met China's President Xi Jinping for the first time, hosting the leader at Mar-a-Lago, his Florida home. The summit was overshadowed by United States missile strikes in Syria.
Mr Alex Jones, whose Infowars website is a hub for the far-right movement but others allege is a wellspring of the "fake news" phenomenon, claimed that Tuesday's attack was launched by the Syrian opposition.
The Admiral Grigorovich RFS-494 crossed through the Bosphorus Strait from the Black Sea, according to an unnamed USA defence official who spoke to Fox News.