The Taliban killed three of those on board - two Afghans and a third foreigner - in an initial firefight and took the rest hostage after the crash yesterday, the defence ministry said in a statement.
The helicopter came down in the Pashtun Kot district of Faryab province, an area partly controlled by the militants, officials said.
The 21 people on board included "three crew members -- two pilots and an engineer, all of them Moldovan nationals," acting Moldovan prime minister Gheorghe Brega told reporters in Chisinau.
The insurgents fought off an initial attempt by the Afghan army to save the surviving hostages yesterday, the ministry said, adding that a fresh rescue bid was launched Wednesday but giving no immediate details.
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The helicopter was an Mi-17 that was privately owned and had been chartered by the Afghan army.
It "made an emergency landing due to technical reasons near Maimana", the defence ministry said in the statement, referring to the capital of Faryab province.
Afghan sources had previously put the number being held at 15.
In a statement on its website Wednesday the Taliban claimed it had shot the helicopter down. The insurgents are known to make exaggerated battlefield claims.
The Taliban said the militants had killed five people and were holding a further 15, and made no mention of any foreign hostages.
It claimed the captives had "been taken to safe areas and are being investigated".
Faryab province has in recent months been the scene of bitter fighting between Afghan security forces and Islamist insurgents, who are increasingly active in northern Afghanistan.
In late September the Taliban temporarily seized control of the provincial capital of Kunduz -- the first time the group had taken control of a major city since being toppled from power in 2001.