Shoppers who bought the lasagne meals, which are produced by French food supplier Comigel on behalf of Findus, have now been warned not to eat them.
Tesco and Aldi withdrew a range of ready meals produced by Comigel over fears they contained contaminated meat.
The FSA said there is no evidence to suggest it is a food safety risk.
Tests have been ordered on the lasagne for the veterinary drug phenylbutazone. Animals treated with "bute" are not allowed to enter the food chain.
An FSA statement said: "The meat content of beef lasagne products recalled by Findus has tested positive for more than 60% horse meat. Findus withdrew the beef lasagne products after its French supplier, Comigel, raised concerns about the type of meat used in the lasagne.
"We have no evidence to suggest this is a food safety risk. However, the FSA has ordered Findus to test the lasagne for the veterinary drug phenylbutazone, or 'bute'."
The company has already started a full recall of its lasagne products.
Findus UK apologised to customers and said anyone who bought the products could get a full refund. A spokesman said: "We would like to reassure you we have reacted immediately."