Kenya could be banned from the Olympics if it does not pass new anti-doping rules by a new World Anti-Doping Agency deadline of 2 May.
Kenya has already missed two deadlines to show it is tackling cheating in sport - 11 February and 5 April.
If Kenya does not legislate to create a new national anti-doping agency, it will be declared non-compliant and move a step closer to missing the Rio Games.
Meanwhile Ethiopia has been given until November to perform mass doping tests.
The two nations are among the most successful in track and field, and placed first and fifth respectively in the medal table at the 2015 World Athletics Championships.
Since 2011, more than 40 Kenyan athletes have failed drugs tests and the country has been placed on a 'watch-list' of nations at risk of breaching the World Anti-Doping Agency (Wada) code and told to take legal steps to toughen its anti-doping procedures.
But while lawmakers have held a preliminary reading of a bill criminalising sports doping, two further hearings and presidential assent are still required and the country's parliament is now in recess.
However, Athletics Kenya's acting president Jackson Tuwei has said he believes Wada is "satisfied with the progress" of the country's anti-doping efforts.
Ethiopia is not in danger of missing the Rio de Janeiro Olympics in August, but could face a ban at a later date if it does not comply with Wada's request to test up to 200 athletes.
Results of the drug tests - to which the government has pledged $300,000 (£212,900) - must be provided to Wada and world athletics' governing body, the International Association of Athletics Federations (IAAF).
"We are told that we could be banned from the IAAF if we don't comply with the request," team doctor Ayalew Tilahun told a news conference.