"It's an extremely deadly organization, very well trained. And it's one of the only al Qaeda affiliates which actually has actively recruited here in the United States," King, R-N.Y., said.
Five Americans are among the wounded, State Department Deputy Spokeswoman Marie Harf said in a statement. There were no reports of any U.S. casualties, Harf said.
But the Australian, British, Canadian, French, Ghanaian and Somali governments have acknowledged the deaths of their citizens, along with Kenyan nationals killed in the "despicable massacre of innocent men, women and children," she said.
British Prime Minister David Cameron is cutting short his annual weekend with the Queen at Balmoral Castle in Scotland to return to London to chair a meeting of the U.K. government's emergency committee dealing with the attacks in Kenya.
Before leaving for Balmoral, Cameron warned the British people they should be braced for "more bad news" from Nairobi.
The Westgate Mall is a destination for Kenya's elite. It bills itself as the city's premiere mall, boasting that it offers customers a "first world interior" and a "safe and serene environment."
It opened in 2007 and has more than 80 stores.
ABC News' Alexis Shaw and The Associated Press contributed to this report.