Obama, who was greeted by enthusiastic crowds in the former capital Yangon, met President Thein Sein, a former junta member who has spearheaded reforms since taking office in March 2011, and opposition leader Aung San Suu Kyi.
The trip is intended to highlight what the White House has touted as a major foreign policy achievement -- its success in pushing the country's generals to enact changes that have unfolded with surprising speed over the past year.
"I've shared with him the fact that I recognise this is just the first steps on what will be a long journey," Obama, with Thein Sein at his side, told reporters after talks with the Myanmar leader at Yangon's old parliament building.
"But we think a process of democratic and economic reform here in Myanmar that has been begun by the president is one that can lead to incredible development opportunities," he added, using the country name preferred by the government and former junta, rather than Burma, which is used in the United States.
Thein Sein, speaking in Burmese with an interpreter translating his remarks, responded that the two sides would move forward, "based on mutual trust, respect and understanding".
"During our discussions, we also reached agreement for the development of democracy in Myanmar and for promotion of human rights to be aligned with international standards," he added.
Tens of thousands of well-wishers, including children waving American and Burmese flags, had lined the route from the airport to catch a glimpse of the U.S. president.
"ICON OF DEMOCRACY"
Obama met fellow Nobel Peace Prize laureate Suu Kyi, who led the struggle against military rule and is now a lawmaker, at the lakeside home where she spent years under house arrest.
Addressing reporters afterwards, Suu Kyi thanked Obama for supporting the political reform process. But, speaking so softly she was barely audible at times, she cautioned that the most difficult time was "when we think that success is in sight".
"Then we have to be very careful that we are not lured by a mirage of success and that we are working towards genuine success for our people," she said.
Obama recalled Suu Kyi's years of captivity and said she was "an icon of democracy who has inspired people not just in this country but around the world".
"Today marks the next step in a new chapter between the United States and Burma," he said. Before he left, the two embraced and he kissed her on the cheek.
Earlier, Obama made an unscheduled stop at the landmark Shwedagon Pagoda, where he, Secretary of State Hillary Clinton and their entire entourage, secret service agents included, went barefoot up the giant stone staircase.
Some human rights groups have objected to the visit, saying Obama is rewarding the government of the former pariah state for a job that is incomplete.
Speaking in Thailand on the eve of his visit, Obama denied he was going to offer his "endorsement" or that his trip was premature.
Obama's Southeast Asian trip, less than two weeks after his re-election, is aimed at showing how serious he is about shifting the U.S. strategic focus eastwards as America winds down wars in Iraq and Afghanistan. The so-called "Asia pivot" is also meant to counter China's rising influence.
Aides said Obama was determined to "lock in" the democratic changes under way in Myanmar but would press for further action, including efforts to curb ethnic and sectarian violence.
A senior U.S. official said Obama would announce the resumption of U.S. aid programmes in Myanmar during his visit, anticipating assistance of $170 million in fiscal 2012 and 2013, but this, too, would be dependent on further reforms.
The United States has softened sanctions and removed a ban on most imports from Myanmar in response to reforms already undertaken, but it has set conditions for the full normalisation of relations, such as the release of all political detainees.
Asked if sanctions could be lifted completely at this stage, a senior administration official insisted they could not. "All these things are reversible," he said.
In a move clearly timed to show goodwill, the authorities in Myanmar began to release dozens of political prisoners on Monday, including Myint Aye, arguably the most prominent dissident left in its gulag.
Some 66 prisoners will be freed, two-thirds of them dissidents, according to activists and prison officials.
In a speech to be given at Yangon University to an audience that will include several high-profile former prisoners, Obama will stress the rule of law and allude to the need to amend a constitution that still gives a great role in politics to the military, including a quarter of the seats in parliament.
Violence between majority Buddhists and the Rohingya Muslim minority in western Myanmar is a top concern, and Obama's aides said he would address the issue directly with Myanmar's leaders.
Myanmar considers the Rohingya Muslims to be illegal immigrants from neighbouring Bangladesh and does not recognise them as citizens. A Reuters investigation into the wave of sectarian assaults painted a picture of organised attacks against the Muslim community.
At least 167 people were killed in two periods of violence in Rakhine state in June and October this year.
Thein Sein, in a letter to U.N. Secretary-General Ban Ki-moon last week, promised to tackle the root causes of the problem, the United Nations said.
Despite human rights concerns, the White House sees Myanmar as a legacy-building success story of Obama's policy of seeking engagement with U.S. enemies, a strategy that has made little progress with countries such as Iran and North Korea.
Obama's visit to Myanmar, sandwiched between stops in Thailand and Cambodia, also fits the administration's strategy of trying to lure China's neighbours out of Beijing's orbit.
(Writing by Alan Raybould; Editing by Alex Richardson)