At least three explosions were heard at the beginning of what authorities believe to be a coordinated attack, Nangarhar provincial governor spokesman Attahullah Khogyani said.
In January, gunmen attacked an office of aid group Save the Children in Jalalabad, killing at least five people and wounding 25.
Afghan security forces surrounded the area and were still battling the gunmen hours after the initial explosions.
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The incursion took place during a weekly mass protest in which thousands of Palestinians gathered along the Israel-Gaza frontier. On Thursday, Hamas leader Yahya Sinwar signaled his support for thousands of Palestinians to breach the border fence.
Kabul has become one of the deadliest places in the country for civilians as security forces struggle to keep the militants at bay following the withdrawal of North Atlantic Treaty Organisation combat forces at the end of 2014.
Militants have staged several attacks across Afghanistan this year.
In Afghanistan, nine people were killed and more than thirty six injured in multiple blasts in Jalalabad on Sunday.
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Stephenson also said in the memo that the company's head of lobbying and external affairs, Bob Quinn , 57, would be retiring. Cohen is also under investigation by prosecutors in NY for possible bank fraud and campaign finance violations.
No one had claimed responsibility for the attack at the time of filing this report.
"I saw two rickshaw drivers on the ground with their arms blown off", said Khan Mohammad, a local resident who saw the initial blasts and the start of the gunbattle.
The Taliban recently launched their annual spring offensive, in an apparent rejection of a peace overture by the Afghan government.
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How will they arrive here and where will they land? Also at play: similarities between Trump and Kim. She said that the idea of the US reducing its military footprint in South Korea wasn't on the table.
Afghan security forces have struggled to combat the Taliban and IS since the USA and North Atlantic Treaty Organisation formally concluded their combat role in the country in 2014, shifting to a support and counterterrorism mission.