The collection of rebel groups fighting to depose President Bashar al-Assad of Syria pushed further south on Friday toward the major city of Homs, moving closer to the capital, Damascus, according to the rebels and a war monitoring group.

The rebels’ stunningly rapid gains spread alarm to neighboring countries, prompting border closures to guard against the prospect of further chaos as Mr. al-Assad’s authoritarian government lost more of its grip over swaths of the country.

And in another sign of the government’s loosening control, a Kurdish-led force backed by the United States, which is separate from the rebels advancing on Homs, said it had deployed in the eastern city of Deir al-Zour, which the government had previously held.

Taken together, the battlefield gains present the most serious challenge in years to Mr. al-Assad’s power.

Despite being largely overshadowed by the wars in Gaza and Lebanon, the Syrian civil war never ended and instead fell into a protracted stalemate. Diplomatic efforts to find a political solution have been stagnant for years.

The coalition of advancing rebels is led by Hayat Tahrir al-Sham, a group previously affiliated with Al Qaeda. Although it split with Al Qaeda in 2016 and has attempted to gain international legitimacy, it is still designated as a terrorist organization by the United States and the United Nations.