Kenyan military forces have been engaging in sporadic gun battles with Islamic extremists holding an unknown number of hostages inside a Nairobi mall.
Officials say 10 to 15 terrorists have been holed up in the mall since Saturday, when they attacked with grenades and assault rifles, leaving 68 people dead and more than 150 wounded.
Somalia's radical rebel group, al-Shabab, claims responsibility for the attack as retribution for the presence of Kenyan troops in Somalia.
Al-Shabab says there will be no negotiations.
A statement from al-Shabab on its official Twitter feed Saturday says the attacks are retribution for military action by Kenya inside Somalia. The group said it was now shifting the battlefield to Kenya.
A witness says that before the attackers opened fire with AK-47s, they told Muslims to stand up and leave because non-Muslims would be targeted. Witnesses says the attackers also threw grenades in the Nairobi mall, which was hosting a children's day event.
According to the Associated Press, U.S. officials say the wife of a foreign service national working for the U.S. Agency for International Development was killed and four American citizens were reported injured.