"The aggression is a flagrant violation of global law, a breach of the worldwide community's will, and it is doomed to fail", said state news agency SANA.
AFP's correspondent in Damascus said several consecutive blasts were heard at 4am, followed by the sound of airplanes overhead.
Major-General Igor Konashenkov is reported to have said: "The Russian Defence Ministry also has evidence that Britain had a direct involvement in arranging this provocation in Eastern Ghouta".
A strike could be carried out by long-range missiles launched from submarines, ships or aircraft and targeted at Syrian military installations.
Immediately after the attack, Syrian regime TV, broadcasting live from the landmark Omayyad Square, showed crowds of civilians mixing with men in uniform, including vehicles with flags. The Barzah district of the city - the location of a major scientific research center - has been rocked by the strikes, another witness told the news agency.
Russian Deputy Prime Minister Arkady Dvorkovich said global relations should not depend on one person's morning mood, in apparent reference to Trump's tweets. The military action is a response to an apparent chemical weapons attack that killed dozens of people earlier this month.
Syrian media claimed that air defenses hit 13 rockets south of Damascus.
And a significant body of information including intelligence indicates the Syrian Regime is responsible for this latest attack.
"Good souls will not be humiliated", Syria's regime tweeted after the airstrikes began.
The US military, assisted by forces from the United Kingdom and France, launched the strikes targeting chemical weapons operations this morning Australian time to punish President Bashar al-Assad for his alleged use of chemical weapons against his people.
"America does not seek an indefinite presence in Syria", he said. We thank them both.
The U.N. -backed Organization for the Prohibition of Chemical Weapons concluded in June 2017 that sarin was the nerve agent used in the attack.
Gen. Joseph Dunford, the chairman of the Joint Chiefs of Staff, said the USA did not coordinate targets with or notify the Russian government of the strikes, beyond normal airspace "de-confliction" communications.
Russian forces in Syrian did not respond; the only opposition to the operation came from Syrian surface-to-air missiles, the general added.
British jets fired missiles at a Syrian military base suspected of holding chemical weapons ingredients on Saturday in Britain's first military action against President Bashar al-Assad's regime.
Trump's United Nations ambassador, Nikki Haley, said the president had not yet made a final decision, two days after he tweeted that Russian Federation should "get ready" because a missile attack "will be coming" at Moscow's chief Middle East ally.
The Syrian regime has repeatedly denied any use of banned weapons.
Trump said he was prepared to sustain the response until Assad's government stopped its use of chemical weapons.