"Any man found engaging in sexual activities with another man should be arrested," Times LIVE
quoted Odinga as saying at a rally on Sunday, in the Nairobi town of Kibera. "Even women found engaging in sexual activities will be arrested."
An August census results had showed the national population was perfectly split between men and women. Odinga, who is also a member of parliament, argued that, with the census result, there was "no need" for homosexuality.
Some critics had argued the new constitution adopted in August contained articles that were tantamount to tolerating same-sex marriages and abortion, but Odinga rejected the accusations.
"Those were lies from leaders who wanted to confuse Kenyans to reject the new law, the Constitution is very clear on that matter. It does not state anywhere that same sex marriage is legal in Kenya," he said.
Neighboring Uganda had moved to introduce a bill that would further criminalize homosexuality and even gay rights advocacy. The move has reportedly been described as "odious" by US President Barack Obama and sparked the ire of rights groups.