He said the US would expand co-operation on economic issues, security and climate change with Indonesia, the world's most populous Muslim nation.
Mr Obama also expressed affection for a country he lived in as a boy.'Build trust'
In a wide-ranging news conference with President Susilo Bambang Yudhoyono, Mr Obama said he had worked hard to repair ties with Muslim communities.
"I think that our efforts have been earnest and sustained. We don't expect that we are going to completely eliminate some of the misunderstandings and mistrust that have developed over a long period of time, but we do think that we're on the right path."
Mr Obama said the US had reached out to Muslims on areas such as education and business to "build trust" and "create more people-to-people contact".
End Quote Barack Obama US President
The only thing that was there when I first moved to Jakarta was Sarinah (a shopping mall). Now it's one of the shorter buildings on the road”
But he added: "I think it's an incomplete project. We've got a lot more work to do."
The US president also criticised Israel's plan to build apartments for Jewish settlers in disputed East Jerusalem.
"This kind of activity is never helpful when it comes to peace negotiations," he said.
Peace talks between Israel and the Palestinians resumed in September after a break of almost two years but were suspended after a few weeks when a freeze on the building of Jewish settlements expired.
Mr Obama will deliver a keynote speech at South East Asia's largest mosque in Jakarta on Wednesday, which analysts say will be his most high-profile attempt to engage the Islamic world since a landmark speech in Cairo in June 2009.Childhood times
Mr Obama said Indonesia had "figured out how to create a genuine democracy" with a hugely diverse population.
Mr Yudhoyono said the pair had signed a "comprehensive partnership" agreement.
"We agreed to improve co-operation in a number of sectors, with the main agenda being trade and investment, education, energy, climate and the environment, security and democratisation," Mr Yudhoyono said.
Mr Obama also referred to his childhood times in Jakarta, saying: "It's wonderful to be here although I have to tell you that when you visit a place that you spent time in as a child, as the president it's a little disorientating.
"I will tell you, though, that I barely recognised it as I was driving down the streets. The only thing that was there when I first moved to Jakarta was Sarinah (a shopping mall). Now it's one of the shorter buildings on the road."
Mr Obama attended schools in Jakarta between the ages of six and 10.
He said he had "great affection for the people" of Indonesia.
"Obviously I have a sister who is half Indonesian, my mother lived and worked here for a long time, so the sights and the sounds and the memories all feel very familiar."
The short trip affords the president little leisure time and the White House has now announced he will leave almost two hours early on Wednesday, so his flight can outrun the volcanic ash cloud thrown up by the recent deadly eruption of Mount Merapi.