In the letter, Kulov asked that his appeal for an early release be forwarded to the Sokuluk district court.
In a statement released this week, Kulov said he was told that the Prosecutor-General's Office had lost the letter.
Aliyev said if the authorities do not respond to Kulov's request by 22 July, Ar-Namys will launch nationwide acts of protest.
"We will conduct [protests]. If the authorities do not give us an answer before the 22nd [of July], we will start [protest] acts," Aliyev said. "They will be in various forms -- meetings, protests, pickets -- in front of the [Kyrgyz] White House, the Justice Ministry, and the department of prison management. The actions will take place in all areas of the republic."
Kulov has announced he will launch a hunger strike on 22 July if authorities do not contact him or Ar-Namys concerning the matter.
Kulov remains one of Kyrgyzstan's best-known political figures and was considered a strong challenger to incumbent President Askar Akaev before his conviction removed him from the country's political scene.
(also with AKIpress report)