The hitherto-unknown Jaish-ul Adl (Army of Justice) said on its website that it was behind Friday's attack, calling it a "severe blow" for the Iranian government.
The assault was launched in response "to the crimes of the Revolutionary Guards in Syria," the group said in a statement, ISNA news agency reported.
Opposition groups in war-ravaged Syria have charged that Tehran is sending members of its elite Revolutionary Guards to fight alongside forces loyal to President Bashar al-Assad.
Tehran said the militants crossed over from Pakistan fled back across the border after the attack.
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Deputy Interior Minister Ali Abdollahi called on the Pakistani government to "take measures to control the border more seriously".
The Revolutionary Guards meanwhile said the incident was "commanded and supported by the intelligence services of the dominant power," referring to the United States.
Sistan-Baluchestan province is home to a large community of minority Sunni Muslims, unlike the rest of Shiite-dominated Iran.
Drug traffickers have also clashed with members of the security forces in Sistan-Baluchestan in the past.