CHICAGO, April 24 (Reuters) - The U.S. government will require dairy cattle moving between states to be tested for bird flu starting on Monday, Agriculture Secretary Tom Vilsack told reporters on Wednesday.

Vilsack said all laboratories and states in the country must report positive tests in cattle for any influenza A, and the U.S. Department of Agriculture (USDA) would pay for increased testing.

The measures come a day after the U.S. Food and Drug Administration said it had found bird flu virus particles in some samples of pasteurized milk, though it said commercial milk supply remains safe.

Positive flu tests in cattle will prohibit animals from being moved during a 30-day waiting period and until they test negative, Vilsack said.

The USDA said last week that cow-to-cow transmission was a factor in the spread of bird flu in dairy herds, but it still did not know exactly how the virus was being moved around.

Dairy herds in eight states tested positive over the past month, along with one dairy worker in Texas. State agriculture officials have said they believed wild birds introduced the virus to cattle. (Reporting by Tom Polansek; Writing by Caroline Stauffer; Editing by Emelia Sithole-Matarise)