The United States was sending more troops to the encircled capital to help evacuate its civilians after the Taliban's lightning advances brought the Islamist group to the door of Kabul in a matter of days. Just last week, a U.S. intelligence estimate said Kabul could hold out for at least three months.
The fall of Jalalabad has also given the Taliban control of a road leading to the Pakistan city of Peshawar, one of the main highways into landlocked Afghanistan.
It followed the Taliban's seizure of the northern city of Mazar-i-Sharif late on Saturday, also with little fighting.
"There are no clashes taking place right now in Jalalabad because the governor has surrendered to the Taliban," a Jalalabad-based Afghan official told Reuters. "Allowing passage to the Taliban was the only way to save civilian lives."
A second security official in the city said the Taliban had agreed to give safe passage to government officials and security forces while they leave Jalalabad.
The decision to surrender was taken to avoid "casualties and destruction", the person added.
After U.S.-led forces withdrew the bulk of the their remaining troops in the last month, the Taliban campaign has accelerated as the Afghan military's defences appeared to collapse.
U.S. President Joe Biden on Saturday authorized the deployment of 5,000 troops to help evacuate citizens and ensure an "orderly and safe" drawdown of U.S. military personnel. A U.S. defence official said that included 1,000 newly approved troops from the 82nd Airborne Division.
Taliban fighters entered Mazar-i-Sharif on Saturday virtually unopposed as security forces escaped up the highway to neighbouring Uzbekistan, about 80 km (50 miles) to the north, provincial officials said. Unverified video on social media showed Afghan army vehicles and men in uniforms crowding the iron bridge between the Afghan town of Hairatan and Uzbekistan.
Two influential militia leaders supporting the government - Atta Mohammad Noor and Abdul Rashid Dostum - also fled. Noor said on social media that the Taliban had been handed control of Balkh province, where Mazar-i-Sharif is located, due to a "conspiracy." read more
In a statement late on Saturday, the Taliban said its rapid gains showed it was popularly accepted by the Afghan people and reassured both Afghans and foreigners that they would be safe.
The Islamic Emirate (Taliban) "will, as always, protect their life, property and honour and create a peaceful and secure environment for its beloved nation," it said, adding that diplomats and aid workers would also face no problems.
CAPITAL INCREASINGLY ENCIRCLED 1/2
As the capital looked increasingly isolated as a government stronghold, Afghans streamed into Kabul, fleeing the provinces and fearing a return to hardline Islamist rule.
Early on Sunday, refugees from Taliban-controlled provinces were seen unloading belongings from taxis, families stood outside embassy gates, while the city's downtown was packed with people stocking up on supplies.
Hundreds of people slept huddled in tents or in the open in the city, by roadsides or in car parks, a resident said on Saturday night. "You can see the fear in their faces," he said.
Western governments were accelerating plans to evacuate their embassy staff, citizens and Afghans who had worked for them.
The State Department has reached out to advocates to request names of Afghans in Kabul who have worked with the Americans and need to be evacuated, two sources familiar with the matter said. The list of names could include journalists and human rights activists.
The British ambassador will leave the country by Sunday evening, UK media reported. The country, which was sending 600 troops, sped up the departure of Britons due to the rising risk that the Taliban would overrun the airport, the reports said.
Biden said his administration had told Taliban officials in Qatar that any action that put U.S. personnel at risk "will be met with a swift and strong U.S. military response."
CLOSING IN ON KABUL
Earlier on Saturday, the Taliban, facing little resistance, took Pul-e-Alam, capital of Logar province and 70 km (40 miles) south of Kabul, according to a local provincial council member, who spoke on condition of anonymity.
Police officials, however, denied reports that the Taliban had advanced closer to Kabul from Pul-e-Alam, which is a staging post for a potential assault on the capital.
Kandahar, the biggest city in the south and the heartland of the Taliban, fell to the militants' control on Friday. Herat, the biggest city in the west and near the border with Iran, also fell on Friday.
Biden has faced rising domestic criticism as the Taliban have taken city after city far more quickly than predicted. The president has stuck to a plan, initiated by Republican former President Donald Trump, to end the U.S. military mission in Afghanistan by Aug. 31.
Biden said it is up to the Afghan military to hold its own territory. "An endless American presence in the middle of another country's civil conflict was not acceptable to me," Biden said on Saturday.
Afghan President Ashraf Ghani on Saturday held talks with local leaders and international partners, including U.S. Secretary of State Antony Blinken. Ghani and Blinken discussed urgent efforts to reduce violence in Afghanistan, the State Department said.
Qatar, which has been hosting so-far inconclusive peace talks between the Afghan government and the Taliban, said it had urged the insurgents to cease fire. Ghani has given no sign of responding to a Taliban demand that he resign as a condition for any ceasefire. Reporting by Kabul and Washington bureaus, Writing by Raju Gopalakrishnan, Alasdair Pal, Cynthia Osterman; Editing by William Mallard