The two-hour assault on Tuesday, which left one Afghan guard dead, was the first time ICRC offices have been targeted in Afghanistan since the organisation began work there 26 years ago.
An International Organization for Migration (IOM) complex in Kabul came under sustained attack less than a week earlier, and the two incidents raise the prospect of a new phase in the Taliban's 12-year insurgency in which no organisation is considered off-limits.
The ICRC, with 1,800 employees nationwide, had 36 staff including six expatriates in Jalalabad, which is close to the Pakistani border and surrounded by some of Afghanistan's most unstable districts.
"All movements have been frozen throughout Afghanistan, there is not a single ICRC delegate or employee that is moving, taking the roads, today," Jacques De Maio, ICRC's South Asia chief, said in a statement released in Geneva on Thursday.
"Our sub-delegation in Jalalabad has been closed, so we are reconnecting with the government and re-connecting with armed groups to determined what happened and why."
Jalalabad lies on the key route from the Pakistani border region -- where many militants are based - to Kabul, and it has been the scene of repeated attacks in recent years.
A message on the ICRC's Twitter page had initially said that all the organisation's activities across Afghanistan had been suspended.
"As a consequence of the attack... people will not be getting valuable help such as food and medical aid," the ICRC said on the social networking site.
The ICRC maintains strict neutrality in the Afghan conflict and was thought to be protected from attack by its working relations with the Taliban and other insurgent groups.
No militant group has claimed responsibility for Wednesday evening's attack, in which one guard died at the start of the two-hour assault.
"He was unarmed, defenceless, he was protecting a compound from where hundreds of thousands of Afghans were getting valuable services," De Maio said in the video statement.
"It was a brutal, despicable and frankly senseless attack... there isn't a single Afghan that would not recognise that we are strictly independent and humanitarian in what we do."
The ICRC provides medical support to two government-run hospitals as well as technical and financial help to 47 clinics across the country run by the Afghan Red Crescent Society.
It also visits prisoners held by both the Afghan authorities and the US-led NATO coalition, to monitor their treatment and living conditions.
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