His political party, All Basotho Convention Party has confirmed receiving the letter.
This comes in the wake of mounting pressure to do so after he was named as a suspect in his ex-wife’ s murder.
The First Lady of the tiny southern African country, Maesiah Thabane, with whom he was having an affair at the time of the murder, was charged in connection with the killing in February.
Lesotho was plunged into political instability this year after the prime minister lost control of parliament. His coalition partners abandoned him.