Information is strictly controlled in the former Soviet republic and state media did not report on the incident.
The reports of clashes could not be independently confirmed but witnnesses told news agencies that there was heavy gunfire throughout the night and the northern suburbs of the capital were surrounded by police.
Other witnesses said that security personnel in armoured personnel carriers were patrolling the streets which remained closed for much of Saturday.
Arkady Dubnov, a Moscow-based reporter for the Vremya Novostei newspaper and expert on Central Asia, told the AFP news agency that sources in Ashgabat had told him of "tanks and armoured vehicles opening fire on a drinking water factory" where an armed group was hiding.
The US embassy in Turkmenistan warned Americans to stay away from the northern districts of the city.
The Central Asian nation, bordering Iran and Afghanistan, has a predominantly Muslim population and large oil and gas reserves.
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