"Five members of the Khodr Abu Hoshar group began a hunger strike on 12 July and are only accepting fluid to drink," security spokesman Bashir al-Daajat said on Sunday.
"This strike is a protest against the state security court's decision to uphold the sentences" given the men in 2000, he said.
The detainees in Qafqa prison, north of Amman, have been on hunger strike for six consecutive days, said Aljazeera's correspondent on Sunday.
Two detainees were admitted to a hospital, he said.
In April, the state security court upheld the death penalty for Khodr Abu Hoshar and Osama Sammar, who were found guilty of planning attacks on Jordanian tourist sites during millennium celebrations.
The men were convicted in September 2000 of plotting to attack tourist sites frequented by Jews and Westerners in Jordan.
The same military court also handed seven-and-a-half to 10-year prison terms to seven others accused of participating in the same plot.
Al-Daajat did not specify which of the men are on hunger strike.
Lawyers for Abu Hoshar, the presumed ringleader of the group, and his co-defendants have said that the verdict was unfair and that testimony and confessions were made under duress.
Initially the group was accused of links to Osama bin Laden's al-Qaida network, but the charge was dropped for lack of proof.