He has been on the run since the military launched its offensive in the region in late April.
Pakistan has offered a $615,000 reward for information leading to Fazlullah's death or capture, and rumours have circulated for weeks that he is critically injured or close to capture.
Fazlullah and his supporters is believed to have beheaded opponents, burned schools and fought against government troops since November 2007.
He is a son-in-law of the pro-Taliban religious leader Sufi Muhammad, who secured a government deal to put three million people in the northwest under the sharia in February.
Taliban members continued to carry arms and marched into the district of Buner in April, putting Fazlullah's fighters within 100km of Islamabad, and Pakistan unleashed its military offensive.
Abbas said that the operation in Swat and two other northwest districts was almost over, but said the Taliban leadership remained elusive, with many disappearing into the mountains.
"We are constantly targeting militant leaders. They always keep themselves protected," he said.
Qamar Zaman Kaira, the Pakistan information minister, said that the area had been cleared of "terrorists", but a military statement issued on Wednesday said that some pockets of resistance remained.
The military claims to have killed about 1,600 fighters in the northwest operation, but the tolls are impossible to verify.
Military and government officials say they will open up a second front against Baitullah Mehsud, Pakistan's main Taliban commander, who is believed to be in the tribal areas along the Afghan border.