He will also be allowed to return to his home in Pretoria, where Reeva Steenkamp was shot and killed.He denies murdering the 29-year-old, saying he mistook her for an intruder.
In the hearing at Pretoria's High Court, Mr Pistorius also sought an end to supervision by a probation officer and compulsory drug and alcohol testing.
The state opposed the application. Mr Pistorius, 26, was not in court for the hearing.
Seeking income
The bail conditions were imposed by Magistrate Desmond Nair on 22 February - including the travel restrictions.
Mr Pistorius was originally ordered to hand over his two South African passports, avoid his home in Pretoria and all witnesses in the case, report to a police station twice a week and to abstain from drinking alcohol.
But they were relaxed but Judge Bert Bam, who described the decision not to grant Mr Pistorius permission to travel as "wrong".
Defence lawyer Barry Roux said the bail conditions amounted to "house arrest".
"Why would this athlete go to a country without extradition and go and hide," he asked the court.
"It is not as if the appellant is travelling for holiday in Mauritius; it's only to gain an income, there's no other reason."
Reports said the athlete had not yet resumed training and had no current plans to compete internationally.
In an unrelated case, the athlete's brother, Carl Pistorius, appeared in court on Wednesday charged with the culpable homicide of a female motorcyclist in a 2008 road crash. He pleaded not guilty and is due to appear in court again next week
BBC
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