Mr Spencer also dismissed reports that members of the group who had been disarmed were not being treated properly.
The rebels - calling themselves the West Side Boys - spoke on Thursday to the BBC's Focus on Africa programme, calling for the release of their supporters from jail and a review of the country's peace agreement.
A total of 11 British soldiers were captured last Friday - five were released on Wednesday.
A British commander says fresh efforts are under way to secure their release.
No demands
The Sierra Leonean Information Minister Julius Spencer told the BBC that the militias had made no demands directly to the government and that the demands broadcast on the BBC would not be met.
He said the government would not be subjected to such pressure.
The militia spokesman, who identified himself as "Colonel Cambodia", was speaking to the BBC on a satellite phone given to the group by the British.
He said their captives were well and being properly fed and provided with adequate medicine and shelter.
He said the six would not be released until their demands are met.
Terms of release
Mr Spencer said current members of the group under arrest were being held for criminal activities and warned the West Side Boys they risked criminal charges if they continued with their actions.
He said all groups who wanted to join the army were to go through the government's disarmament programme.
Mr Spencer also dismissed reports that members of the group who had been disarmed were not being treated properly.
British officials said negotiations were continuing to secure the release of the remaining hostages.
The BBC correspondent in Freetown, Mark Doyle, said five of the British soldiers were released at about the same time as the satellite phone became available to the West Side Boys.
He said it is possible that the five were effectively swapped for the communications equipment.
The troops, from the Royal Irish Regiment, were captured by the West Side Boys last Friday. The group's spokesman said the troops entered their area of operations without permission.
British army officials have not made public the details of how the release of the five soldiers was secured, and in particular whether it or the Sierra Leonean Government had made any concessions in return.
British military spokesman Tony Cramp said: "We have done no deal with the West Side Boys."
Freed
The five released soldiers have arrived in Freetown after being set free on Wednesday.
A British Army spokesman, Brigadier Gordon Hughes, said the men were resting after being debriefed at a military barracks in the capital.
"They were naturally tired. They have been taken to a place where they can recover and get some rest. They were medically checked. They are fit and well," he said.