The animals died during the first circuit of the gruelling four-and-a-half-mile course. Ornais fell at the fourth and Dooneys Gate fell at the sixth, Becher’s Brook. Just 19 of the 40 starters finished the race.
The latest deaths have prompted campaigners to call for an end to the historic race, with some describing it as little more than animal cruelty on the same level as bullfighting.
Animal Aid director Andrew Tyler: “We’ve heard claims that the Aintree course is being made safer, safer, safer. No it’s not.
“The Grand National should be banned. It’s a deliberately hazardous, challenging and predictably lethal event.”
He said the race’s combination of a tightly packed field, high fences, long distance and huge crowd noise meant it was extremely dangerous for the horses taking part.
He added: “It’s a depraved spectacle, on a par with Spanish bullfighting. It is straightforward animal abuse.”
The League Against Cruel Sports said there had been 17 deaths at the National in the last 16 years.
A spokeswoman said: “It is hugely distressing but sadly not surprising that there were two fatalities in this year’s Grand National. There is no way the race can reasonably continue in its current form.
“Surely it’s time for commonsense to prevail and for the course to be drastically changed to prevent these needless deaths every year on racing’s national day of shame.”
Last week celebrities including Queen guitarist Brian May, BBC DJ Mark Radcliffe and wildlife presenter Bill Oddie sent an open letter to The Guardian newspaper calling for the public to boycott the race.
Tony Moore, chairman of Fight Against Animal Cruelty in Europe, said: “I don’t see a solution by altering the fences, it really has to be an outright ban.
Julian Thick, managing director of Aintree Racecourse, said the Grand National was a well-organised and professional race.
Grand National coverage: Sports Monday, Page 13.