WASHINGTON — Secretary of State Rex W. Tillerson sought to mend fences with Africa on Tuesday as he embarked on a five-nation tour across the continent, promising $533 million in new aid just months after President Trump disparaged some African countries with a vulgar term.

In a speech before leaving Washington, Mr. Tillerson trumpeted American efforts to improve access to electricity across Africa and provide critical drugs for millions of people to treat H.I.V./AIDS. He did not mention, however, that the Trump administration has proposed slashing funding for both programs, along with other aid efforts seen as vital in Africa. Mr. Tillerson is scheduled to visit Ethiopia, Djibouti, Kenya, Chad and Nigeria.

Though it will be his first trip to the continent as secretary of state, Mr. Tillerson noted that “in my previous life, I spent quite a bit of time in Africa.”

As chief executive of Exxon Mobil, Mr. Tillerson was known as a take-no-prisoners negotiator who pushed deals in African countries such as Nigeria, Equatorial Guinea, Chad and Angola that have been widely accused of corruption and poor human rights. Exxon Mobil received stinging criticism for its work with the government in Nigeria, in particular.