Some 164 people were killed and more than 2,300 were displaced in Kenya, Tanzania, Madagascar, Seychelles, and Somalia after the disastrous 2004 Asian tsunami.
The waves are expected to hit the Kenyan coast, a popular tourist destination, at about 1700 GMT, officials said. One person in Kenya was killed in the 2004 tsunami.
"The government of Kenya has consequently issued a tsunami warning for the people living along the Kenyan coastline," Esther Murugi, the minister of state for special programmes said in a statement.
"The water levels are expected to rise up to 2 to 3 metres in areas of Malindi, Lamu, up to Kiunga while in Kilifi, Mombasa up to Shimoni, the levels are expected to rise up to 2 metres," she said.
Senior Assistant Director at Kenya's Met office, Ali Mafimbo, said an alert had been issued to keep people on the lookout and to stay out of the sea once they saw water levels receding.
Tanzania said it expected waves of up to 1.5 metres to hit the coastline between 1600 GMT and 1800 GMT.
"There will likely be huge waves in the Indian Ocean � all fishermen and other vessels should keep off the sea," Tanzania's Meteorological Agency director, Agness Kijazi, told Reuters.
"People should evacuate coastlines, especially in northern parts of the country."
Madagascar's National Office for Disaster and Risk Management said they did not expect the tsunami to cause damage on the Indian Ocean island.
"We don't expect the wave to have a big impact on Madagascar. We are not planning to move anybody. We urge people not to panic," Louis de Gonzague Rakotonirainy said, before the latest wave of aftershocks.
"In the event the situation develops, the inhabitants of the east coast will be advised to move to higher ground. A meeting is taking place right now to evaluate the situation."
(Reporting by Humphrey Malalo and Yara Bayoumy in Nairobi; Fumbuka Ng'wanakilala in Dar es Salaam; Alain Iloniaina in Antananarivo; Writing by Yara Bayoumy; Editing by James Macharia)
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