Both districts, Garmser and Naway-e Barakzayi, are in the southern province of Helmand.
Earlier today, Afghan Deputy Interior Minister Abdul Malik Sidiqi said Afghan forces had pushed the militants out of Naway-e Barakzayi late on July 17.
Speaking to Radio Free Afghanistan, Sidiqi also accused Pakistani militants of taking part in the July 16 attack in Garmser district. He said the Pakistani fighters included militants from the Islamic groups Lashkar-e Tayyaba and Jamiat Ulema-e Islami.
"Unfortunately from some neighboring countries, particularly Pakistan, terrorist groups cross the border to Afghanistan," Sidiqi said. "One of these terrorist groups is called Lashkar-e Tayyaba and the other, Jamiat-e Ulema Islami. These groups have directly attacked the [Garmsel] district [of Helmand Province] and have burnt the Afghan flag. Inshallah, the security forces will severely punish these foreign aggressors."
Helmand Deputy Governor Amir Mohammad Akhunzada said up to 400 Afghan soldiers are being deployed alongside foreign coalition troops to recapture the Garmser district.
Earlier, an Afghan official said that around 4,000 Afghans have fled violence between coalition forces and Taliban militants in Helmand Province "in the past few days."
Rahilla Zafar, an official for the International Organization for Migration, said many of the displaced Afghans have gone to neighboring Kandahar Province.
(with AP, AFP, Reuters, dpa)