Israel has not made any statement on the strike. The US, France and Great Britain have also said they were not involved in the operation.
The attack came two days after Syrian government forces allegedly gassed at least 60 civilians to death in a chemical attack in Douma.
Defense analysts say there are large deployments of Russian forces at the T-4 base and Russian jets fly regular sorties from the base to strike rebel-held areas such as Douma.
US Secretary of Defense James Mattis warned Monday that he has not ruled out American military action in response to the chemical attack.
U.S. President Donald Trump said he was meeting with military and other advisers and a decision would be made within 48 hours and might come as soon as the end of the day.
"Nothing is off the table," he said when asked if U.S. military action was a possibility.
Asked if Russian President Vladimir Putin bore any responsibility for the attack, Trump said, "He may, yeah, he may. And if he does it’s going to be very tough, very tough."
The Syrian government and it’s ally Russia have denied involvement in the chemical attack and have charged that reports of chemical use are false.
The UN Security Council in New York was set to meet late Monday afternoon to discuss the attacks.
On Sunday, Defense Minister Avigdor Liberman indicated that when it comes to Syria he always operates under the assumption that Israel acts alone.
Two US officials told NBC that Israel carried out the strike and that the US was informed in advance.
Russia and Syria have also accused Israel of striking the Tiyas Military Airbase, also known as the T-4.
Located near Homs, it is the largest Syrian airbase. It is believed to house an Iranian complex that that supplies arms to Tehran’s ally, Lebanon's Shi'ite Hezbollah.
It is believed that Israel also hit this same base in February of this year.
To prevent any clash between Moscow and Jerusalem with regard to Syria, Russian President Vladimir Putin and Prime Minister Benjamin Netanyahu established a deconfliction mechanism in September 2015.
Jerusalem has said repeatedly in the past that it will not allow Iran to build a permanent military presence inside Syria and the Israeli Air-Force in the past has struck arms convoys transferring weapons from Iran to Hezbollah.
In spite of the Kremlin’s statement Diplomatic officials stressed on Monday that the Israeli-Russian deconfliction mechanism has not broken down as a result of the strike on the T-4 and the hotline between Jerusalem and Moscow is still working.
Kremlin spokesman Dmitry Peskov told reporters in Moscow that President Vladimir Putin had no contact with Israel with regard to the airstrikes, the Russian media website Sputnik International reported.
Russian defense and foreign ministries have demanded an explanation from Israel, according to Sputnik.
According to the Russian News Agency TASS, the country’s Foreign Minister Dimitry Lavrov told reporters that the Israeli strike could have dangerous consequences. I hope at least the military of the US and those countries, which are part of the US-led coalition, understands this.”
He had as similar reply to US warnings Sunday about a possible military strike in response to the chemical attack.
Dmitri Trenin, the Director of Carnegie’s Moscow Center tweeted, “The US and Russia are now closer to a direct collision between their military forces than at any time since the Cold War. The only question on my mind: will Russia hit back at the US when it launches strikes against Damascus?”
According to reports from the Russian Defense Ministry and Syrian media, two Israeli F-15 combat jets launched eight missiles at the airbase from Lebanese airspace. Syrian forces shot down eight of the missiles and three others hit their targets.
The Syrian Observatory for Human Rights said that at least 14 people were killed in the strikes, including three Iranians.
Four Iranian military personnel were killed in an air strike on a Syrian air base on Sunday, Iran’s Fars news agency said.
Some Iranian media reported that one of those killed was a member of the Revolutionary Guards Aerospace Force, a division that operates drones.
Reuters contributed to this report.