Associated Press reporters in Damascus heard heavy airstrikes overnight and into Tuesday on the city and its suburbs. Photographs circulating online showed destroyed missile launchers, helicopters and warplanes.
There was no immediate comment from the insurgent groups — led by Hayat Tahrir al-Sham, or HTS - that have taken control of Damascus.
Israel had earlier seized a roughly 400-square-kilometer (155-square-mile) buffer zone inside Syria that had been established after the 1973 Mideast war, a move it said was taken to prevent attacks in the aftermath of the overthrow of President Bashar Assad.
Israel has also said it is striking suspected chemical weapons sites and heavy weapons to prevent them from falling into the hands of extremists. Israeli officials rarely acknowledge individual strikes.
Israel has a long history of seizing territory during wars with its neighbors and occupying it indefinitely, citing security concerns. Israel captured the Golan Heights from Syria in the 1967 Mideast war and annexed it in a move not recognized internationally, except by the United States.
The Britain-based Syrian Observatory for Human Rights, which has closely tracked the conflict since the civil war erupted nearly 14 years ago, said Israel has carried out more than 300 airstrikes across the country since rebels overthrew Assad over the weekend, ending his family's half-century rule.
The Observatory, and Beirut-based Mayadeen TV, which has reporters in Syria, said Israeli troops are advancing up the Syrian side of the border with Lebanon. It was not possible to independently confirm the reports.
Lt. Col. Nadav Shoshani, an Israeli military spokesperson, said "the reports circulating in the media about the alleged advancement of Israeli tanks towards Damascus are false." He said Israeli troops are stationed within the buffer zone in order to protect Israel.
Israel's military had previously said troops would enter the buffer zone "and several other places necessary for its defense."
Israeli media meanwhile reported that the air force was methodically destroying Syria's military assets to ensure whoever rules the country next would have to rebuild them.
The operations "have been systematically destroying all that remains of the escaped tyrant's military," wrote Yossi Yehoshua, the military correspondent for Israel's largest daily, Yediot Ahronot.
"Dozens upon dozens of targets, including arms depots of various kinds, have been hit in waves of attacks so as to prevent them from falling into hostile hands and from posing a threat to Israel." The air force "currently enjoys complete freedom of action," he added.
Egypt, Jordan and Saudi Arabia have condemned Israel's incursion, accusing it of exploiting the disarray in Syria and violating international law.
"The assaults carried out by the Israeli occupation government, including the seizure of the buffer zone in the Golan Heights, and the targeting of Syrian territory confirm Israel's continued violation of the principles of international law and its determination to sabotage Syria's chances of restoring its security, stability and territorial integrity," the Saudi Foreign Ministry said in a statement Tuesday.
Saudi Arabia has been in talks with the United States in recent years over normalizing relations with Israel in exchange for a U.S. defense pact, American assistance in establishing a civilian nuclear program and a pathway to the establishment of a Palestinian state.
But the kingdom has also repeatedly condemned Israel's actions in the Gaza Strip, where it is at war with the Hamas militant group. Last month, Saudi Arabia's crown prince and day-to-day ruler Mohammed bin Salman accused Israel of committing genocide in Gaza, allegations Israel adamantly rejects.