Mr Obama said the decision did not indicate a lack of concern, and said that he and Prime Minister Najib Razak had spoken about human rights.
The US had condemned Mr Anwar's sodomy conviction as politically motivated.
Meanwhile, the two leaders have agreed to upgrade diplomatic ties to a "comprehensive partnership".
Mr Najib said this would entail greater collaboration on the economy, security, education, science and technology.
Mr Obama, the first serving US president to visit Malaysia for nearly 50 years, said the two countries are at the start of a "new era of partnership".
'Core belief'The president was asked during a news conference with Mr Najib why he had not made any comment about Mr Anwar's case.
He said: "The fact that I haven't met with Mr Anwar is not indicative of a lack of concern."
Instead, he stressed that both the US and Malaysia still had work to do on civil liberties and political reform.
Mr Obama, who spent some of his childhood in neighbouring Indonesia, said he had shared with Mr Najib his "core belief" that societies that respect civil rights will be more successful in the 21st Century.
America's national security adviser Susan Rice is due to visit Mr Anwar later in the week.
On Sunday morning - in hot and muggy weather - he visited the National Mosque of Malaysia in black socks, removing his shoes in keeping with protocol.
He stopped for a few moments in a prayer room with his head bowed.
Mr Obama will end his visit by speaking to young people from around South East Asia at a town hall meeting.
His visit to the region comes at a tense time as China's assertive stance in territorial disputes has its smaller neighbours on edge.
Ahead of his visit, Malaysia's government-controlled newspapers printed the US flag on their front pages, along with the words "Welcome, Mr President".