The Taliban claimed responsibility for the attack in a text message sent to media.
The attack in one of Afghanistan's main cities comes ahead of a presidential election on April 5, and demonstrated the attackers' determination to disrupt the vote.
The assault began with two explosions just before dawn targeting the police station and a nearby square, close to compounds used by international organizations including the United Nations.
The initial attack was carried out by two suicide bombers, one of them driving a three-wheeler vehicle.
The Nato-led force in Afghanistan sent helicopter gunships to support Afghan security forces as a fire fight raged for over three hours before they were able to clear the area of the remaining militants.
Police said they shot dead six Taliban, and all of them wore suicide vests.
"From today's attack in Jalalabad so far, we have received 11 dead bodies and 22 wounded," the head of the provincial hospital, Humayoun Zahir, told Reuters.
A police district chief was among the dead, according to Fazel Ahmad Shirzad, police chief for Nangahar province. The wounded included an Afghan assigned to a security detail for UN staff and the offices of a local radio and television broadcaster were also damaged in the attack, according to a security source.
The militants have threatened to kill anyone participating in the election, and have stepped up attacks in heavily populated areas including the capital Kabul since the start of the year.
Security forces discovered at least two roadside bombs on the heavily guarded highway between Jalalabad and Kabul on Wednesday, and carried out controlled explosions.
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Its 200% true until and unless Pakistan, India, Iran and Afghanistan doesn't seriously and honestly agree to stop any such violent activities, targeting, killing and blame game the peace and prosperity of the South Asian region is impossible and also a great threat to the world. All four countries must act seriously and must respect each other sovereignty and integrity. Its dead sure that in any such activities or motivation behind such activities comes from such sources. Alternatively the UNO and all civilized member nations enforce them to stop either direct or indirect support of such criminal acts against each other and must respect each other integrity else UNO must stop all Aid and support to these four countries until and unless they seriously becomes civilized human.