The 800-meter world champion said in a statement that she had agreed to the request by Athletics South Africa to wait for the results of the tests, which are expected in June.
Semenya said she still believed she should be allowed to compete but had reflected on the events of the past week. She was prevented from running in a competition near Cape Town last Tuesday and responded by threatening legal action.
"I believe that the decision to bar me from competing in Stellenbosch last week was unlawful and wrongful," Semenya said in the statement. "I have, however, considered the request by Athletics South Africa (ASA) that I await the conclusion of the International Association of Athletics Federations' (IAAF) processes by the beginning of June this year before I return to competitive athletics."
The 19-year-old South African, whose lawyers had said they would file legal papers against ASA if they did not clear her to run, said she wanted confirmation from the IAAF that her situation would be clarified by the beginning of June.
"I welcome ASA's public statement that it will ensure that the IAAF is held to its undertaking to complete its processes by the beginning of June," Semenya said. "I trust that ASA will do the honorable thing and stick to its word in this regard.
"I have also instructed my legal representatives to seek confirmation by the IAAF that it will complete its processes by the beginning of June. I also trust that this will be forthcoming."
IAAF spokesman Nick Davies said Tuesday that he could only reiterate the track body's official position on Semenya.
"No comment until the case is concluded," Davies said.
Semenya had been expected to demand permission from the ASA to, near Johannesburg, on Tuesday. ASA has upheld a request by the IAAF to not allow Semenya to run competitively until her "medical process" has been completed.
Semenya has not competed since she blew away the field to win the 800-meter gold medal at the world championships in Berlin last August.
Her dramatic improvement in times and muscular build led the IAAF to order gender tests. The IAAF has refused to confirm or deny Australian media reports that the tests indicate Semenya has both male and female sex organs.
Last week, Semenya's patience appeared to have run out when she appeared at a Yellow Pages Series event in Stellenbosch, near Cape Town, and requested permission to run.
An ASA official at the meet refused. Semenya's lawyers then said they would file legal action "soon" in a bid to get the teenager back on the track.
Semenya's camp has now apparently backed down.
"Together with my coach and agent, I have therefore decided that I will return to competitive athletics at the EAA meeting to be held on 24 June in Zaragoza, Spain," Semenya said. "I reiterate that based on medical and legal advice, I am firmly of the view that there are no impediments to me racing in female athletics competitions."