Iraqi military officials and state television reported that Syrian government forces retook control of the remote Rabiya crossing between the two countries after rebels pulled out.
Gen. Qassim al-Dulaimi, commander of Iraq's forces around the border region of al-Qaim, also reported the sounds of fighting at the Bukamal crossing, suggesting Assad's troops are trying to retake that one as well.
The fighting in Damascus and Aleppo has shaken the government's once seemingly iron grip on the two cities, which are both home to elites who have benefited from close ties to Assad's regime, as well as merchant classes and minority groups who worry their status will suffer if Assad falls.
Col. Abdul-Jabbar Mohammed Aqidi, the commander of rebel forces in Aleppo province, said "we gave the orders for the march into Aleppo with the aim of liberating it."
"We urge the residents of Aleppo to stay in their homes until the city is liberated," he said in a video posted by activists on YouTube. He added that rebels were fighting inside the city while others were moving in from the outskirts.
Aqidi called on government troops to defect and join the opposition, and said rebels will protect members of President Bashar Assad's Alawite minority sect, an off-shoot of Shiite Islam, saying "our war is not with you but with the Assad family."
The Britain-based Syrian Observatory for Human Rights and Aleppo-based activist Mohammed Saeed said the fighting is concentrated in several neighborhoods.
Saeed said rebels are in full control of the central Salaheddine district and the nearby Sakhour area. He added that thousands of residents have fled tense quarters of the city for safer neighborhoods and the suburbs.
"Aleppo is witnessing serious street battles" and many shops are closed, Saeed said.