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Hezbollah, which supports Syrian President Bashar Assad in the six-year-old conflict, said in a statement the strike would not demoralize the Syrian army or negatively affect its allies.
The U.S. military action was a "service" to Israel and its "ambitions in the region," Hezbollah added, without elaborating.
The Syrian opposition applauded the attack, but said it must not be a one-off and was not enough on its own to stop government warplanes from hitting rebel-held areas.
The Syrian opposition has long criticized the United States for failing to protect rebel-held areas from government air strikes, demanding the creation of a no-fly zone or the provision of anti-aircraft weapons to rebel groups.
U.S. President Donald Trump's decision to launch missiles at the airbase, from which he said a deadly chemical weapons attack had been launched, marked a dramatic departure from the more cautious approach of his predecessor Barack Obama. It was welcomed by opposition officials, but they called for more.
"One airbase is not enough. There are 26 airbases that target civilians," tweeted Mohammad Alloush, a senior rebel official. George Sabra, a prominent opposition politician, told al-Hadath TV: "The truth is that militarily, if it is limited to this strike, then it has no meaning."
The Free Syrian Army, a loose alliance of rebel groups that includes factions that have received military support from the United States, called the U.S. strike the "correct starting point" for finding a "just political solution" to the war
"We view that the responsibility of the United States is still great, and does not stop with this operation," it added in a statement, warning that the Damascus government and its allies could commit "acts of revenge" against civilians.
American officials described the attack - the first direct U.S. assault on the government of President Bashar al-Assad in six years of civil war - as a one-off that would not lead to wider escalation. Syrian officials and their allies also said they did not expect the attack to lead to an expansion of the conflict.
The strikes targeted the base at Shayrat, 40 km (25 miles) southeast of Homs city, from which Washington and Syrian opposition groups say Syrian warplanes launched a chemical weapons attack on the town of Khan Sheikhoun this week.
The Syrian government has strongly denied responsibility and says it does not use chemical weapons. The Homs governor said on Friday the base was being used to provide air support for operations against Islamic State east of Palmyra.
Hassan Haj Ali, commander of the Free Idlib Army rebel group, which fights under the FSA umbrella, told Reuters the strikes came at a "very important phase" and showed Syrians that "there is still humanity in this world". He said he did not expect further such U.S. attacks, however.
Nasr al-Hariri, chief negotiator of the High Negotiations Committee (HNC), said on Twitter that the strikes "should they continue, would kick off a correct start in combating terrorism".
The Saudi-based HNC, the main opposition body which includes political and armed groups, has participated in U.N.-sponsored peace talks in Geneva.
"We hope for the continuation of the strikes in order to prevent the regime from using its planes to launch any new air raids or going back to using internationally banned weapons," said Ahmad Ramadan, head of the media office of the Syrian National Coalition political opposition group.
"The airbase targeted by the U.S. strike was used to kill Syrians," Ramadan said. The American attack "sends a clear message to the regime and its backers" that they can no longer avoid repercussions, he added.