In a video on Tuesday, the group accused the hostages of working for the Iranian army, intelligence service and the Red Crescent.
The video showed the seven hostages and one of their captors, who threatened to kill the hostages unless the Iranian government releases five colleagues of the group.
The tape showed the hostages declaring their identities and urging Iranian officials to help.
The group also claimed responsibility for what it called the Zabul Operation, in which 22 Iranian soldiers were killed, a group member said in the video.
Zabul is a town in Iran's Sistan-Baluchistan province near the border with Afghanistan.
The toll matched the number of soldiers the Iranian government said were killed in an ambush by Afghan bandits between Zabul and Sistan-Baluchistan's capital, Zahedan, on Thursday night.
On 19 January, the group claimed the execution of one of nine Iranian soldiers it kidnapped along the Pakistani border in December. The Iranian government announced on 29 January that the other soldiers were freed.
Iran has accused the United States and Britain of sponsoring Thursday's cross-border raid that resulted in the death of Zahedan's governor. Tehran also warned Afghanistan and Pakistan to crack down on what it called Afghan bandits.
The southeastern province is notoriously lawless and is regarded as a key transit route for opium and other drugs from Afghanistan and Pakistan headed for Europe and the Gulf.