The attack, which comes as the Taliban step up their annual spring offensive, began around midnight, with the insurgents capturing one district and parts of another, local provincial council member Jamila Amini told AFP Tuesday from inside the city.
"The Taliban are moving very fast, if the government does not take serious and speedy action, the province is going to collapse to Taliban", said Hamidullah, a resident of the city reached by telephone.
In January, NATO's Resolute Support Mission, tasked with building up the Afghan government's security forces, assessed that almost 15 percent of the country's 407 districts - more than 20 percent of the landmass - was under insurgent control or influence, according to a watchdog report released this month.
Early Tuesday, Ahmad Zaki, a doctor at the city's central hospital, said that so far two dead police officers and 16 wounded security forces members had been brought to the medical facility since the start of the latest assault.
Mujahid said Taliban fighters launched a multipronged attack and overran a large number of checkpoints belonging to Afghan security forces in the city.
Mohammad Sarwar Osmani, a lawmaker form Farah province, also confirmed the Taliban attacks.
The province, which also borders the opium-rich Taliban heartland of Helmand province, has key smuggling routes into Iran.
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A resurgent Taliban, largely dependent on narcotics revenues, has expanded its territorial control over parts of Afghanistan since the withdrawal of most global combat forces at the end of 2014.
But inside the city residents reported clashes were continuing.
Satar Hissaini, a tribal elder in Farah, told AFP: "The situation is very bad".
"There were eight terrorists who carried out a coordinated attack in Jalalabad city, killing ten people", Khogyani said.
Farah is a poppy-growing province in an isolated region of Afghanistan. Local residents fear the whole province may fall to the insurgents. There are plans for a section of the multi-billion-dollar TAPI (Turkmenistan, Afghanistan, Pakistan and India) gas pipeline to traverse it.
Taliban issued a statement to declare that they have captured checkpoints and an office of intelligence department where senior police officials worked.
In 2017 insurgents tried to overrun the capital three times, according to the Afghanistan Analysts Network.