Two of the three teenagers charged over the murder of Australian baseball player Chris Lane have been refused bail by an Oklahoma court.

James Edwards, 15, and Chancey Luna, 16, were both charged with first-degree murder. The third teenager, Michael Jones, 17, was charged with using a vehicle to facilitate the discharge of a weapon and being an accessory after the fact of murder in the first degree.

The former Australian deputy prime minister Tim Fischer – who played a leading role alongside former prime minister John Howard in changing Australia's gun laws after the 1996 Port Arthur massacre – has urged Australian tourists to boycott the US to send a message about gun control.

"Tourists thinking of going to the USA should think twice,'' Fischer said.

"I am deeply angry about this because of the callous attitude of the three teenagers [but] it's a sign of the proliferation of guns on the ground in the USA."

Bail for Jones was set at $1m (A$1.1m). Under Oklahoma law the three boys will be tried as adults. Edwards and Luna face a life sentence if convicted.

Lane was out jogging when the three teens allegedly drove up behind him and shot him once in the back before driving off. Witnesses rushed to Lane's aid but the 22-year-old was pronounced dead in hospital about an hour later.

Prosecutors believe Luna fired the shot that killed Lane. Neither he nor Edwards displayed emotion during the appearance, Australian Associated Press reported. Jones broke down when told he was facing a long prison sentence.

District attorney Jason Hicks told the Shepherd County courthouse that Edwards was treating the murder as a joke. "I believe he is a threat to the community and should not be let out," Hicks said.

Edwards was reportedly already on probation, and had been in court on the day of the murder to sign documents.

The parents of the two younger boys told US media they believed their sons were innocent.

Police chief Dan Ford told media that the boys had killed Lane out of boredom in the final days of their school holidays.

Lane, from Melbourne's Oak Park, was in Oklahoma on a baseball scholarship to a local college. He and his American girlfriend, Sarah Harper, had been back in the US for only three days after visiting family in Australia.

On Monday Lane's family asked the media for privacy.

"There's not going to be any good to come out of this, because it was just so senseless," said Lane's father, Peter.

"There wasn't anything he could have done. It's happened, it's wrong and we'll just try and deal with it the best we can."