Speaking at a breakfast for Paris marathon and world half-marathon athletes at the State House, Kenyatta said the government had made the bill a priority and he was giving it close attention.
"By next week (at the) latest, the Anti-Doping Bill will have been passed by Parliament and I will have signed it into law so that there will be no excuse to deny our team from participation in the Rio de Janeiro Olympics in August," he said.
"We know there are people who are looking for excuses to ensure that Kenya does not participate in the Olympics. We will not give them that excuse," he was quoted as saying in an official news release.
Kenya was given a one-month extension on April 7 to comply with the WADA code or face sanctions that could include a ban from this year's Rio Games.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The African nation, famed for its distance runners but tarnished by around 40 doping cases in recent years, missed a February deadline to establish a legal framework for its Anti-Doping Agency of Kenya (ADAK).
Kenyatta said Kenyan athletes had brought pride and international recognition to the country and outlined the financial rewards on offer to Olympic medal winners.
The president said gold medallists would get 1 million Kenyan shillings (6,955.4 pounds), silver medallists 500,000 and bronze 250,000.
Kenya's Cyprian Kotut won the Paris marathon on April 3 and Geoffrey Kamworor retained his world half-marathon title in March.
Kenya won 11 medals at the 2012 Games in London -- two golds, four silver and five bronze. David Rudisha won the men's 800 metres and Ezekiel Kemboi the men's 3,000m steeplechase.
(Reporting by Alan Baldwin, editing by Ed Osmond)
