"If the peace agreement is over, it is over from one side – the NCP side," Minnawi said.
He said he was considering closing his office in Sudan's presidential palace in protest at the action.
Mohammed Bashir Abdullah, the head of Minnawi's office, said it was the first time the army had launched a direct attack on his men.
The SLA said the new offensive started a week ago and had continued daily.
Areas controlled by SLA fighters have been attacked by government troops in the past, but Khartoum has denied carrying out any military action.
Leaders from three other rebel groups confirmed the attacks near Tabit, at least 50km southwest of el Fasher, north Darfur's capital, and said that other clashes with government forces had occurred across the region.
'Residents fleeing attacks'
Sherif Harir, an SLA member, said: "Bombing has been continuing up till now," adding that air attacks had forced residents to flee 200 villages in the remote area.
Peacekeepers confirmed there had been fighting between government and rebel forces in which aircraft were involved.
"The reports that we have indicate there has been heavy fighting," Kemal Saiki, a spokesman for the joint UN-African Union mission in Darfur (UNAMID), told the AFP news agency.
"We do not have exact details. But with reports of more than 100 vehicles with troops, this is not just a skirmish."
Richard Williamson, the US' special envoy to Sudan, said the new fighting was unacceptable at a time when efforts were being made to bring a ceasefire to the country's troubled western region.
"The government should honour the ceasefire. This descent into violence causes grave concern about the humanitarian situation," he said.
The UN has said up to 300,000 people have died and more than 2.2 million have fled their homes since the conflict erupted in February 2003.
Sudan says 10,000 people have been killed.
The war began when ethnic minority rebels took up arms against the Arab-led Khartoum regime and state-backed Arab militias, fighting for resources and power.
The conflict has since deteriorated with the emergence of a multiplying array of rebel groups, breakaway militia groups and bandits.