The group of 16 were on their way to attack industrial and tourist targets in the country, says the Foreign & Commonwealth Office (FCO).
They were arrested while crossing into Tunisia from Libya.
In a separate incident, a house belonging to the Minister of the Interior was attacked and four policemen were killed.
All travellers should stay away from Chaambi Mountain National Park and all but essential travel should be avoided to the towns of Nefta, Douz, Médenine and Zarzis near the Algerian border.
“The country is undergoing transition following the revolution in 2011,” said an FCO spokesman.
“The potential is there for conflict and further protests, but these are generally not targeting expats or tourists, but some incidents can set off anti-Western demonstrations from time to time.”
Around 330,000 British expats and travellers visit Tunisia each year.
Deadly virus outbreak
Elsewhere, the FCO is continuing to warn expats and visitors to West Africa about an outbreak of the Ebola virus.
Guinea has seen more than 225 cases which have resulted in 143 deaths.
Although the World Health Organisation reports the number of reported cases is falling, the incubation period for the disease is three weeks, so more cases are likely to arise.
The disease is also spreading to neighbouring countries.
Liberia has reported 35 suspected cases and Sierra Leone has identified three cases.
The Ebola virus symptoms include high temperatures, headaches and joint and muscle aches.
The disease is not often found in humans, but is prevalent in apes, monkeys and bats.
One theory is the disease has crossed over from humans eating infected bushmeat.
Hurricane threat to World Cup warm-ups
The hurricane season may lead to England’s World Cup warm up tournament in Miami facing cancellation, says the FCO.
The bad weather season starts in June, but so far no signs of high winds and storms have been detected.
England play Ecuador and Honduras in Miami on June 4 and June 7.
The FCO also points out that the Sun Life Stadium, the venue for the matches, has no public transport links. Taxis from Miami cost $50 and parking is $25.
Florida traffic laws also ban carrying an open alcohol tin or bottle anywhere other than in the boot of a car.