The new push comes after the military in recent weeks took 250 square kilometers (100 square miles) from IS, the command said, bringing the government forces closer to the town of al-Bab.
But it also risks a showdown with Turkish troops and Syrian opposition fighters who have jointly been trying to capture the ISIS-held town for weeks.
Such a showdown had been avoided while government forces were tied up driving rebels out of the eastern sector of the city of Aleppo, the provincial capital. That had allowed Turkey to wage war against IS and also Syrian Kurdish groups in northern Syria.
After President Bashar Assad's victory in Aleppo in December, his military turned its focus on the rest of the province. Assad, backed by Russia and Iran, has vowed to reassert his control over the entire country.
Ankara considers the Syrian Kurdish forces an extension of the Kurdish insurgency within its own borders. The Turkish-backed troops in northern Syria have repeatedly clashed with the U.S.-backed Kurdish fighters, who are leading the battle to retake the nearby city of Raqqa, the Islamic State group's de facto capital.
After the Syrian military's announcement, the opposition forces allied with Turkish troops said they had taken four more villages around the town of al-Bab.
The shifting front lines could also undermine peace talks and a rebel coalition on Thursday desisted from committing to Feb. 20 negotiations in Geneva, which are led by the United Nations.
The coalition of Free Syrian Army factions and other rebels, said it could not "take any step toward a fair political solution without a cease-fire."
It demanded that Russia, Turkey, and Iran step up to their obligation to enforce a cease-fire for Syria, something the three regional players pledged to do at talks in the Kazakh capital of Astana last month. The rebels said at the time they had presented a mechanism to monitor the cease-fire to the Russians and were expecting a response within a week.
"We cannot accept any invitation to negotiations that lead to meaningless outcomes, instead of fair outcomes and a full (political) transition," they said in a statement released on social media.
Associated Press writer Philip Issa in Beirut contributed to this report.