"Initial information shows that at least two gunmen have taken position inside the office of the Red Cross and gunfire is continuing, there has also been an explosion," provincial government spokesperson Ahmad Zia Abdulzai told AFP.
"One Afghan guard has been killed," he added.
Local officials said that a suicide bomber had blown himself up at the gate of the ICRC office and two more insurgents entered the building.
An International Committee of the Red Cross (ICRC) spokesperson in Kabul was unable to give any immediate details.
The attack came on the same day that Afghan security forces killed six militants who stormed the Panjshir provincial governor's office in a brazen pre-dawn assault in one of the country's most stable areas.
The Taliban launched their annual "spring offensive" last month, vowing to use suicide blasts to inflict maximum casualties and destabilise President Hamid Karzai's Us-backed regime.
The attacks followed a major assault on Kabul on Friday, when the Taliban launched a suicide and gun strike on an international compound in the city centre and triggered a battle that lasted several hours.
All four militants, one policeman and two civilians died in that incident.
The effectiveness of Afghan security forces is crucial to the government's ability to defeat the Taliban insurgency as 100,000 NATO-led combat troops prepare to withdraw by the end of 2014.
The police, army and special forces are being trained up by the international coalition, but there are widespread fears that they will not be able to impose security after 12 years of war.
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