After talks in Nairobi, President Obama and Kenyan counterpart Uhuru Kenyatta said they were "united against terrorism" and efforts to deal with it.
But the two leaders differed sharply in their positions on gay rights.
While Mr Obama spoke strongly against discrimination, Mr Kenyatta said Kenya did not share the same values.
Earlier Mr Obama praised Africa's economic and business potential in a speech.
"Africa is on the move... People are being lifted out of poverty, incomes are up (and) the middle class is growing," he told a business summit.
BBC Africa Live: Obama in Kenya as it happened
He also visited a memorial for those killed in the 1998 US embassy bombing.
The trip, which began on Friday, is Mr Obama's first visit as president to the country where his father was born.
Barack Obama said he was encouraged by statements President Kenyatta had made about the need to root out corruption.
People were being "consistently sapped by corruption at a high level and at a low level" and there was a need for "visible prosecutions," Mr Obama said, to show Kenyans that action was being taken.
"They don't have to be a forensic accountant to know what is going on."
Police officers and civil servants had to be paid properly to help curb corruption, but sometimes it just required "breaking the habit".
Unlike some other Western leaders, Mr Obama neither lectured Mr Kenyatta nor patronised him at their joint press conference.
Instead, he spoke like a friend - that Kenya needed to stamp out corruption to attract investments and to make life easier for its own businessmen who have to pay bribes. And Mr Obama pointed out that the US was also once badly affected by corruption, but it had overcome the problem, giving hope to Kenyans.
What Kenya needs, Mr Obama said, were "visible prosecutions".  Will Mr Kenyatta make sure that this happens or will it be business-as-usual after Mr Obama leaves?
As for gay rights, Mr Kenyatta left the clear impression that Kenya will not legalise homosexual relations.  Mr Obama is likely to continue to speak in favour of gay rights, but there was no indication that the issue could cause a serious rift between the two countries.
President Obama had told the BBC he would deliver a blunt message on gay rights when he travelled to Africa - and defended his stand in response to a question at the joint news conference.
"If somebody is a law-abiding citizen, who is going about their business... and not harming anybody, the idea that they are going to be treated differently or abused because of who they love is wrong. Full stop," he said.
But Uhuru Kenyatta said gay rights were not "foremost" in the minds of Kenyans.
There were "some things that we must admit we don't share - our culture, our societies don't accept," he said.
"It's very difficult for us to be able to impose on people that which they themselves do not accept."
In other comments, President Obama said:
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The US president has urged Kenya to hold "visible" trials to tackle corruption, which he said could be the "biggest impediment" to further growth.