AMSTERDAM, Netherlands (AP) _ The Dutch and British, renowned dog lovers, have been outraged by attacks on children and many want their governments to outlaw dangerous breeds.

As legislators in both countries search for ways to accomplish it, even deadlier breeds are being developed.

One of every three Dutch homes has a dog, so the public shock was intense when the family pit bull killed Jack Vrielink, an Amsterdam toddler. It was the second fatal pit bull attack on a Dutch child in less than three months.

After the Vrielink child's death, the government agreed to consider legislation banning the sale and breeding of pit bulls. Agriculture Minister Gerrit Braks had said previously that a ban was not enforceable because the pit bull was not a formal breed.

Pit bulls, which weigh about 45 pounds, were created for organized dogfights and derive from the English Staffordshire bull terrier, a dogfighting favorite in the 19th century.

In Britain, an outcry against rottweilers arose in February when three of them savaged three children in a crowded playground.

Last year, dogs killed three people in Britain, including an 11-year-old girl who was training the two rottweilers that attacked her.

Rottweilers, which are related to the German shepherd and weigh about 110 pounds, number about 100,000 in Britain.

Owners of rottweilers and pit bulls say they are not inherently savage, but sometimes are trained to be.

According to animal protection groups, most owners are people in the lower socio-economic classes who buy the dogs as status symbols and for protection in high-crime areas.

''Fearful Britain's Answer to America's Handgun'' was the headline in the Independent, a British newspaper, on a story about the rottweiler craze.

Prime Minister Margaret Thatcher's government abolished dog licensing two years ago, in keeping with its philosophy of reduced government, and defeated an opposition attempt this month to revive it.

Breeds now being developed include so-called ''bandogs,'' a cross between the stout, broad-jawed pit bull terrier and a larger breed, like the rottweiler.

Britain's Royal Society for the Prevention of Cruelty to Animals calls the cross a ''Darwinian nightmare'' that can kill any unarmed human.

''Bandogs and other crosses being bred at the moment are more savage than anything that we've seen in the past, so we must act quickly,'' Benno Brugink, spokesman for the Dutch Agriculture Ministry, said in an interview.

When asked in March about the possibility of outlawing the bandog, Home Secretary David Waddington of Britain said: ''I am prepared to look at anything.''

The Netherlands put a leash law into effect March 1 and several communities have passed ordinances that require pit bulls to be muzzled. Owners generally ignore the ordinances.

A ban on crossbreeds, or even strict regulation, is problematic because they are difficult to classify or identify.

Defenders of pit bulls and rottweilers say the difference between a pet and a killer lies in training, not the dog's genetic makeup.

''The pit bull is by nature an honest and reliable dog,'' said Jan Dirk van Ginneke, chairman of the Dutch Pit Bull Terrier Club. ''It is merely trained for aggression.

''It's not the dogs that should be punished with a ban, but the owners who keep them for the wrong reasons.''

Van Ginneke, who runs an auto repair shop, has five bulldogs, a pit bull named Happy and a collection of rare birds.

''Five years ago, there weren't even 2,000 pit bulls in the Netherlands,'' said Dik van Oers, chairman of the Netherlands Animal Protection Society.

''Now we have at least five times as many and about 20 percent of them have been bred for aggression to the point of being totally screwed up mentally.'' The Netherlands has about 30,000 rotweillers.

Belgium has only about 100 pit bulls, but advised local governments in 1988 to ban them.

Zele, a small Flemish town, was among the first to do so.

Mayor Mayor Jozef de Bruyne said: ''I never saw a pit bull and I don't think there are any in this town. Let's just keep it that way.''