Golani said that the directions they have received from al-Qaeda chief Ayman al-Zawahri are "not to use Syria for attacks against the West and Europe."
"The directions that we are received from Dr. Ayman, may God protect him, are that the Nusra Front aim is to bring down the regime and its allies, I mean Hezbollah," Golani, whose face was not shown during the interview, said.
He added that the "directions we have received until now is not to target the west and America." He said al-Qaeda might be doing so but not the Nusra Front.
The Nusra Front has made gains in northwestern Syria alongside other insurgent groups in recent weeks, seizing the city of Idlib, the town of Jisr al-Shughour and bringing them closer to government-held coastal areas north of the capital.
"We will continue our focus on Damascus and on toppling this regime," Nusra's Abu Mohamad al-Golani told news channel Al Jazeera in a rare interview aired on Wednesday. "I assure you, Assad's fall won't take a long time."
His warning to Alawite villages and uncompromising language will do little to dispel Western fears about the growing influence of hard-line insurgents in Syria and Nusra's loyalty to al Qaeda. The Alawite community, of which Assad is a member, is an offshoot of Shiite Islam.
The Sunni Muslim Nusra Front is the most powerful faction in Syria opposing both Assad and the Islamic State.
It was not clear where the interview took place and Golani's face was not shown. He sat on an ornate chair opposite the interviewer with his back to the camera.
Addressing the Alawite community, he said: "If they drop weapons, disavow Assad, do not send their men to fight for him and return to Islam, then they are our brothers," he said.
Golani said the Alawites were part of a sect that had "moved outside the religion of God and of Islam." He also said Nusra Front were not at war with Christians and that his group received no foreign state funding.
A black flag used by the group was placed on the table between him and the interviewer from the Qatar-based channel, which did not ask about reports that Nusra might distance itself from al-Qaeda.
Earlier this year, sources told Reuters that Nusra Front's leaders had considered cutting ties with al-Qaeda to form a new entity backed by some Gulf Arab states trying to topple Assad.
Sources within and close to Nusra said that Qatar was encouraging it to go ahead with the move, which would result in more support from Gulf states hostile to both Assad and Islamic State.
Golani also condemned the Lebanese Shiite group Hezbollah, which backs Assad, saying Hezbollah knew its fate was linked to the Syrian leader and its efforts to save him were in vain.
Nusra Front is listed as a terrorist organization by the United States and has been sanctioned by the UN Security Council, but it is more powerful than the mainstream groups favored by Washington and its Arab allies in the fight against both Islamic State and Assad's government.
US-led forces have carried out air strikes that have hit Nusra Front targets, saying they were targeting a specific al-Qaeda-linked faction called "Khorasan Group".
Golani said there was no such thing as Khorasan Group in Syria. "We only heard about this name when the Americans said it," he said.
He said Nusra Front's fight was with Assad and Hezbollah, not the West. But when pressed, said that all options were open if US-led forces continued to target it.
Apart from its recent battlefield gains in the northwest, Nusra Front is a major force in fighting against government forces and allied militia around the northern city of Aleppo. It is also fighting in southern Syria and its fighters have frequently clashed with Islamic State in a number of locations.
Reuters and the Associated Press contributed to this report.