"We can confirm that a number of insurgents have entered the building," said Attaullah Khughyani. "Who they are, and what their target is, is still not clear."
He said there appeared to have been at least three attackers, two of whom had blown themselves up while at least one was still fighting.
Heavy gunfire could be heard from around the building of RTA, Afghanistan's national broadcaster, located close to the provincial governor's compound.
Jalalabad is the capital of Nangarhar, the eastern province on the border with Pakistan where ISIS fighters have established a stronghold, but there is also a strong Taliban presence in the region.
Insurgents fighting to oust the Western-backed government in Kabul have conducted a series of high-profile attacks this year on targets including Afghanistan's largest military hospital and a military base in the northern city of Mazar-i-Sharif.
(Reporting by Rafiq Shirzad; writing by James Mackenzie; Editing by Clarence Fernandez, Robert Birsel)