Farah province, 695 km west of Kabul and bordering Iran, has been the scene of heavy clashes between Taliban and security forces over the past few months.
Abdullah said in parts of the country Afghan soldiers have been surrounded by Taliban for months, but in recent days the National Security Council and the Supreme Commander meetings were not held to address soldiers' problems and to send them support.
Chairman of the provincial Council Fared, Bakhtawar said that terrorists attacked several checkpoints, a result of the attack killed at least 30 security personnel, however, the number of victims will probably increase.
"There is no fear of losing Farah city to the militants", he said, adding that Special Operations Forces and army commandos together with army reinforcement have arrived in Farah city.
"The Taliban are roaming around and fighting in various areas of the city".
Inside the city residents reported clashes were continuing.
"The people are running from the city and the situation is very bad", said a resident of Farah.
A senior Afghan police official, reached by telephone inside Farah city, described the government's situation as "out of control" and predicted the insurgents would renew their offensive under cover of dark, when air support was less effective against them.
Interior ministry spokesman Najib Danish said the Afghan air force was also taking part in the fighting.
"First 1,000 Taliban insurgents attacked Farah districts on Tuesday and after the first attack over 1,000 other insurgents also joined the attack", he said. A total of 43 Taliban fighters were killed during the battles in three different districts, he added.
"NDS forces in their headquarters are engaged in heavy clashes with the Taliban".
The official spoke on condition of anonymity because he was contradicting official government reports.
Farah is a poppy-growing province in an isolated region of Afghanistan. Despite the pressure of greatly stepped-up USA and Afghan airstrikes, the Taliban have shown little interest in the Afghan government's offer of a comprehensive peace agreement.
There are plans for a section of the multi-billion-dollar TAPI (Turkmenistan, Afghanistan, Pakistan and India) gas pipeline to traverse it, a project with which the Taliban have pledged to cooperate.
Farah is home to about 50,000 people and would be the second city to fall to the Taliban since the city of Kunduz fell twice in 2015 and 2016.
Although the insurgents have been unable to take and hold any provincial centre, they are active across Afghanistan and the government has firm control over no more than 56 percent of the country, according to US estimates.