At least 16 people, including journalists, were wounded in the attack.
Jalalabad is the capital of Nangarhar, the eastern province on the border with Pakistan, where the Islamic State fighters have established a stronghold.
"Islamic State fighters are now carrying out an attack inside the state broadcasting building in the city of Jalalabad", the movement's AMAQ newsagency said in a statement on instant messaging service Telegram.
At least 14 people were injured in the attack, the provincial health services director Najibullah Kamawal said, seven of whom have been treated in hospital and since released.
Wednesday' assault in Jalalabad, capital of Nangarhar province, began with bombers blowing themselves up, making way for others to enter the building of national Radio Television Afghanistan, or RTA, officials and witnesses told local journalists.
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The RTA office in Jalalabad is located in the heart of the city close to the headquarters of the provincial government and the main market.
"Three attackers are dead and so are three other people, including one policeman", reported Al Jazeera.
It was not immediately clear who was behind the attack. Earlier, he said there had been three attackers.
The Taliban also has a strong presence in the area but the group said it was not involved.
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