Lavrov said Assad has made it clear he will not step down and demands for him to do so will only result in more violence, Britain's Guardian newspaper reported Friday.
"Either we have to want to save lives and ... forget about who is responsible for the time being, and to bring all of them to the negotiating table, or we don't care about lives and care about [Assad's] fate," Lavrov said in an interview with German broadcaster ARD.
Lavron, conceding reforms offered by Assad were inadequate, said the president was offering a dialogue the rebels should accept because they have not offered any alternatives.
"The only thing which is uniting the opposition is toppling the regime," he said. "In almost two years [the opposition] never produced any constructive platform."
Rebels are acting against the government in parallel "with quite a number of terrorists groups," Lavrov said.
Rebels with al-Qaida-linked fighters said they had nearly full control of an oil-rich northeast region Friday, the third big gain claimed by them this week.
The reported takeover of the hotly contested Hasaka province -- a fertile, rich area 375 miles northeast of Damascus near Iraq -- came with critical assistance from the Sunni Islamic and jihadi militant al-Nusra Front after three days of bitter fighting, the Britain-based opposition Syrian Observatory for Human Rights said.
At least 100 members of the Syrian armed forces and 30 al-Nusra fighters, including five from Kuwait and Iraq, were killed in a pitched battle for the strategic Hasaka province town of Shadadah near a giant oil field, the observatory said.
With Shadadah's fall, "the regime could lose complete control of the province of Hasaka," anti-Assad activist Omar Abu Layla told The New York Times.
Al-Nusra Front, also called Jabhat al-Nusra, is a 13-month-old extremist Islamic group with 6,000 to 10,000 fighters, known for its combat skills.
The United States designated it a terrorist group in December for suspected ties to al-Qaida in Iraq, which is reputed to want to marginalize Shiite Muslims and establish a "pure Islamic state." Assad's Alawite sect is an offshoot of Shiite Islam.
Al-Nusra Front -- which claimed responsibility for 43 suicide attacks in Syria last year -- accounts for about 9 percent of the Free Syrian Army's total fighters, up from 3 percent in August 2012 and 1 percent at the beginning of last year, a non-governmental group tied to a more moderate FSA wing told the U.S. State Department in November.
British Foreign Secretary William Hague told a British defense and security think tank Thursday Syria had become "the No. 1 destination for jihadists anywhere in the world today."