Attahullah Khogyani, spokesman for the governor of Nangarhar province, said the attack targeted a provincial office in Jalalabad.
Inamullah Miakhial, spokesman for Nangarhar regional hospital, said one person was killed and at least 14 wounded.
The casualty count might rise as a gun battle was continuing, he said.
The attack started with a suicide bomber and was followed by gunfire, said Mr Khogyani.
The attack follows a weekend siege of the Intercontinental Hotel in the capital Kabul in which 22 people were killed, including 14 foreigners.
Eleven of the foreigners who died during the Taliban's 13-hour siege worked for the private Afghan airline KamAir.
During a ceremony at Kabul's airport on Wednesday the bodies of seven Ukrainian citizens were handed over to officials for transfer to Ukraine.
Mirwais Samadi, head of the consulate department of the Afghanistan Foreign Ministry, said the attack was launched by “terrorists” and their supporters.
“Some of our countrymen were martyred and some foreign nationals also were killed,” he said. “We express our condolences and thoughts to the victims and families. ”
In eastern Ghazni province, four Afghan police were killed after their checkpoint came under attack by insurgents, said Arif Noori, spokesman for the provincial governor.
Six insurgents were killed and three were wounded in the battle in Dayak district, said Mr Noori.
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