ASMARA, July 10 (Reuters) - Eritrea has accused "fringe" religious groups of sowing dissent in the Red Sea state and defended its right to arrest members who assemble illegally.

In an interview posted on the ruling party's Web site late on Monday, presidential advisor Yemane Ghebremeskel said most of these groups had received "secret or undeclared" foreign funds.

"Most of them went against the national fabric ... to penetrate and sow division within the traditional faiths," he was quoted as saying.

"The government cannot interfere in people's religious beliefs ... but we had problems with a handful of 'new faiths' of a few fringe groups that are alien to the society at large. We have to be clear about the distinction."

About half Eritrea's 4.6 million people are Christian and half Muslim, but only religious groups officially registered with the government can practise.

The authorities routinely deny persecuting anyone on the basis of faith, but have been accused by human rights groups and the U.S. State Department of violating religious freedoms.

Foreign religious groups have criticised Asmara over the appointment of a new head of the Eritrean Orthodox Church and the arrest of some 80 people in May, including several U.S. citizens, in a raid on a religious ceremony.

Yemane said the government's reaction to new religious groups had been "measured".

"The periodic arrests, which are distorted and exaggerated, occur when members of these fringe groups assemble illegally," he said. "When you talk about mass arrest of believers, I am puzzled at the hyperbole. What is mass arrest? Who were the 'mass people' allegedly detained from time to time?"

Yemane singled out the Jehovah's Witnesses, saying the group did not take part in a 1993 referendum giving Eritrea its independence and objected to mandatory national service.

"They cannot have it both ways: refuse to recognise the government but at the same time ask legal services from the same government," he said.