Agriculture Minister Andrew Muir said officials have been asked to explore any potential financial support to assist farmers with such animals.
There have now been four confirmed detentions of BTV which is spread by biting midges.
Chief Veterinary Officer Brian Dooher said the relaxation of movement restrictions had come after a further risk assessment, following completion of surveillance testing in the TCZ.
“With surveillance testing having now ended and noting we are now within the vector inactive period, I can confirm that we are able to relax the restrictions on movements inside and outside the zone,” he said.
“However, certain categories of cattle, sheep, goats, deer, llamas and alpacas will require other measures to qualify for movement, and I would urge farmers to familiarise themselves with those details on the Daera website.”