The SSRC's facility in Masyaf, allegedly involved in the production of non-conventional arms as well as medium- and long-range scud missiles, has been targeted multiple times over the past year by air strikes blamed on Israel.
In an interview on army radio on Tuesday, Israel's Intelligence and Transportation Minister Yisrael Katz welcomed Asbar's "departure from the world".
Israel has not commented on the assassination.
According to a senior official from a Middle Eastern intelligence agency, the Mossad had been tracking Asbar for a long time.
Wreckage of a building described as part of the Scientific Studies and Research Centre (SSRC) compound in the Barzeh district, north of Damascus, in a photo from April.
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The deceased was known for close ties with Syrian President Bashar al-Assad as well as the Iranian regime and according to British-based Syrian Observatory for Human Rights, the unit was being used chemical weapons development.
In April 2017, the United States Treasury Department slapped 271 staff members of the SSRC with sanctions in April of a year ago.
After the Syrian government carried out what independent inspectors said was a sarin gas attack that killed as many as 100 people in the town of Khan Sheikhoun in 2017, Washington also imposed sanctions on 271 individuals associated with the centre.
After hundreds of people were killed in chemical attacks near Damascus in August 2013, a landmark deal with Russian Federation was struck to rid Syria of its chemical weapons stash, staving off USA airstrikes.
Also clarifies that "brigade of special purpose" Abu Amara - before they have attacked Assad controlled by the objects stated in the Telegram, set and detonated the explosive devices with the objective of killing Asber.
The attack comes as Syrian troops regain territory along the 1974 demarcation line separating the Israeli-occupied Golan Heights from Syria.