He said civilians, prisoners and members of security forces were among the victims.
Mohammad Idres, one of the prisoners trapped inside and contacted by cellphone, said he could see about four bodies on the ground outside. “We are very hungry, it’s very hot and we don’t have water,” he said.
“Sometimes it is quiet and then firing starts. The security forces cannot seem to advance because the attackers hold strategic points, including the watchtowers.”
IS claimed responsibility for the attack, which came a day after the Afghan intelligence agency said special forces had killed a senior IS commander near Jalalabad, the provincial capital of Nangarhar.
Officials said Afghan Chief of Army Staff Lieutenant General Yasin Zia arrived on Monday to oversee the operation, involving special forces, to clear the IS fighters holed up inside the prison.
Three militants were killed during the initial attack and gunbattle overnight, while at least 21 civilians and members of security forces died in the fighting, and 43 were wounded, Attaullah Khugyani, a spokesman for the governor said.
As the siege dragged through the day, the normally bustling city was placed under a curfew.
Some 130 kilometres east of Kabul, Jalalabad lies on the highway leading to the Khyber Pass and the Pakistani city of Peshawar.
A United Nations report last month estimated there were about 2200 IS members in Afghanistan, and that while the group had lost territory and its leadership had been depleted, it remained capable of carrying out high-profile attacks.