Tennis players are to be given 48 hours to tell the authorities if they are approached about throwing matches and risk punishment if they fail do so.
Murray says some players struggle to make ends meet
The new 48-hour rule will be adopted by the board of the ATP Tour at its next meeting in November, and will be backed up by a new 'integrity unit'.
Murray told BBC 5live he believed some tennis matches are being fixed - and that all the players are aware of it.
The ATP has already said it will ask to meet Murray to discuss his comments.
I've always defended a clean sport and that's the way I see tennis
The Scot said: "It is pretty disappointing for all the players, but everyone knows that it goes on.
"It's difficult to prove. They can try their best until the last games in each set and then make some mistakes, hit a couple of double faults and that's it."
The ATP confirmed that it would look into these claims as a matter of great importance, and that it was working with the sport's other authorities on setting up an integrity unit.
"We have asked Andy Murray, through his agent, for a meeting as soon as possible to discuss the claims made public," said a tour spokesman.
"Nothing is more important than the integrity of our sport and the ATP has shown that it will act where it has information which requires investigation.
"It will become a sanctionable offence for a player not to provide information that helps the police and the authorities.
"If a player is approached they need to pass on that information within 48 hours.
It is the responsibility of everyone, without exception, to ensure we have any information about possible threats to the integrity of tennis
"Our anti-corruption programme has stringent procedures in place to deal with any suspected corruption.
"It is the responsibility of everyone, without exception, to ensure we have any information about possible threats to the integrity of tennis."
World number one Roger Federer cast some doubt on Murray's claim, saying: "We've all heard the rumours but I don't know where they could have come from.
"To speak in these terms you've got to have proof and I can't add anything to this subject. I've always defended a clean sport and that's the way I see tennis."
In an investigation for 5live Sport, leading betting companies have expressed concern about the results of several games.
And Murray believes the chance to make extra money is too much for some players to turn down.
He added: "There are some guys who have to come to tournaments every single week and out of their first-round-loser's cheque - about 2,500 euros - they have to pay for their air fares.
"A career lasts probably only 10 or 12 years and you have to make all your money while you're still playing. But it's not really acceptable."
Last month Tim Henman told BBC One's Inside Sport programme he has heard of players being asked to influence the outcome of matches.
"I personally have never experienced it but, listening to the players talking, it seems it goes on," said the former British number one.
In August, online betting exchange Betfair voided the market on Nikolay Davydenko's match with Martin Vassallo at the Poland Open because of concerns over unusual betting activity.
The ATP Tour launched its own probe as a result.