Israel carried out a wave of heavy airstrikes across Syria as its troops advanced deeper into the country, a Syrian opposition war monitor said Tuesday. Israel denied its forces were advancing toward Damascus after they pushed into a buffer zone inside Syria following the overthrow of President Bashar Assad.

Associated Press reporters in the capital heard heavy airstrikes overnight and into Tuesday on the city and its suburbs. Photographs circulating online showed destroyed missile launchers, helicopters and warplanes.

Syrian insurgents who toppled President Bashar Assad said they won't impose any religious dress code on women and vowed to guarantee personal freedom for everyone.

In a statement posted on social media, the insurgents' General Command said “it is strictly forbidden to interfere with women’s dress or impose any request related to their clothing or appearance, including requests for modesty.”

Israel conducted strikes Monday targeting positions of the deposed Syrian government's army including in Damascus, the south and the coast, a war monitor said, the latest in a series of attacks since rebels took over a day earlier.

"Israeli strikes targeted military sites, including weapons depots housing anti-tank missiles and anti-aircraft weapons," Rami Abdel Rahman, who heads the Britain-based Syrian Observatory for Human Rights war monitor told AFP. "Israel is deliberately destroying anything it perceives as a threat," he added.

U.S. National Security Advisor Jake Sullivan will travel to Israel this week for talks on Syria following the fall of Bashar al-Assad, and on a truce deal in Gaza, the White House said Monday.

Sullivan will meet Israeli officials to discuss "efforts to reach a hostage release and ceasefire deal in Gaza, the latest developments in Syria, and for discussions about Lebanon and Iran," National Security Council spokesman Sean Savett said.

Hundreds of Syrian refugees gathered at two border crossings in southern Turkey on Monday, eagerly anticipating their return home following the fall of President Bashar Assad's government.

Many arrived at the Cilvegozu and Oncupinar border gates at daybreak, draped in blankets and coats. Some camped by the barriers of the border crossing, warming themselves with makeshift fires or resting on the cold ground. The border crossings correspond to the Bab al-Hawa and Bab al-Salameh gates on the Syrian side of the border.

Across Lebanon, the Middle East, and beyond, the fall of Syria’s authoritarian government at the hands of Islamist-led rebels set off waves of jubilation, trepidation and alarm.

Many Lebanese exulted at the overthrow of the Syrian leader while others worried about more instability rocking a region in turmoil.

Israel's Foreign Minister Gideon Saar said Monday that his country's military takeover of the buffer zone along its border with Syria was a "limited and temporary step".

"This is a limited and temporary step we took for security reasons," Saar said in a press conference at the foreign ministry in Jerusalem. Israeli Prime Minister Benjamin Netanyahu announced on Sunday that he had ordered the army to "take control" of the zone after the fall of Syrian president Bashar Al-Assad.

Prime Minister Mohammed Ghazi Jalali, who remained in his post after Assad and most of his top officials vanished over the weekend, has sought to project normalcy.

“We are working so that the transitional period is quick and smooth,” he told Sky News Arabia TV on Monday, saying the security situation had already improved from the day before, when joyful crowds gathered in public squares and celebratory gunfire rang out across the capital.

A Syrian opposition war monitor says a top aide to the brother of Syria’s ousted president was found dead in his office near the capital, Damascus.

The Britain-based Syrian Observatory for Human Rights said Maj. Gen. Ali Mahmoud, who was in charge of Maher Assad’s office, had led a 2018 military campaign in southern Syria.

The Turkish-backed forces, known as the Syrian National Army, launched an offensive against the Syrian Democratic Forces in the northern Syrian city of Manbij on on Dec. 6, days after similarly expelling the SDF fighters from the city of Tal Rifaat.

Turkish security officials said Monday that “control of Manbij has been secured,” without providing further detail. The officials provided the information on condition of anonymity, in line with Turkish regulations.