"We will not tolerate such behaviors in the country," the BBC quoted Raila Odinga as saying. "The constitution is very clear on this issue and men or women found engaging in homosexuality will not be spared."
Africa Review reported that Odinga told a rally in Nairobi on Sunday that "if found the homosexuals should be arrested and taken to relevant authorities."
The website said that Odinga added it was "madness" for two men to fall in love with each other when a recent census showed there were "plenty of women" in the country.
However, Odinga's spokesman said Monday that the prime minister was quoted out of context and that he was only highlighting that the country's constitution bans same-sex weddings.
Kenya's largest gay rights organization said the comments sparked panic among its members.
'Extortion, blackmail and violence'
Nguru Karugu, a board member with the Gay and Lesbian Coalition of Kenya, said Monday the group had received calls from concerned members, some of whom are HIV-positive and fear they will be arrested when they collect life-prolonging medicine from government clinics.
David Kuria, another activist with the organization, told the BBC that he believed the prime minister's remarks would provoke "extortion, blackmail and violence."
Kenya's laws prohibit "sex against the order of nature." That charge is punishable by up to 14 years in prison.