Alusala said that the rebel leader's coming to South Africa had to be "taken at face value" until Machar's actions suggested otherwise.
"We know that in July this year there was an altercation between Machar's troops and the government's troops. Machar in that period made his way on foot to the Democratic Republic of Congo, where he traveled for 37 days, so for a journey of that nature a person would need medical attention.
"We have been informed that he also sought medical attention in Khartoum and the fact that he is now traveling to South Africa makes sense as the medical infrastructure in South Africa is well developed, therefore it could be purely for medical care that he is going to SA. So it is unfair perhaps at this stage to speculate that he has traveled for any other reasons, Alusala said.
Devastating civil war
Reports on Wednesday quoted Machar as saying that his stay in South Africa would be temporary and that he would leave after the tests.
"I am leaving the country now for South Africa to have medical tests and after that I will leave South Africa," he told reporters at Khartoum airport in Sudan without specifying where.
He did not, however, give details of his medical condition.
Machar was reportedly discharged from hospital in Khartoum on August 26 after being treated for a swollen leg.
Khartoum, according to reports, was a longtime backer of Machar during the two-decade war that led to South Sudan's independence in 2011.
Machar led a breakaway faction that fought the mainstream pro-independence rebels and received arms from the Sudanese military.
He broke again with the Juba government in 2013, sparking a devastating civil war in which allegations of gang rape, cannibalism and mass killings of civilians were widespread.
He returned to Juba earlier this year under a hard-won peace deal but it broke down in July when fresh clashes broke out between his ethnic Nuer supporterd and the mainly Dinka troops of the government.