Citing an informed source, BBC Persian had earlier reported that friends had been unable to contact her, and there were fears for her safety.
The International Federation of Sport Climbing (IFSC) said it had been in contact with Rekabi and was "trying to establish the facts".
The IFSC, in a statement, said it had also been in contact with the Iranian Climbing Federation.
"The IFSC fully support the rights of athletes, their choices, and expression of free speech".
Last year, she won the bronze medal in the women's combined event at the 2021 IFSC Climbing World Championships.