US Secretary of State Hillary Clinton has pledged to improve ties with Burma if current reforms continue.
After meeting Burmese President Thein Sein, Mrs Clinton said the US would reward Burma's leaders if they kept "moving in the right direction".
After talks with Mr Thein Sein in the remote capital, Nay Pyi Taw, Mrs Clinton met pro-democracy leader Aung San Suu Kyi in the main city, Rangoon.
The US maintains tight sanctions on senior leaders in Burma's hierarchy.
But a series of reforms this year has led to speculation that decades of isolation could be about to end.
"The United States is prepared to walk the path of reform with you if you keep moving in the right direction," Mrs Clinton said.
"These are incremental steps and we are prepared to go further if reforms maintain momentum. In that spirit, we are discussing what it will take to upgrade diplomatic relations and exchange ambassadors," Mrs Clinton told reporters.
"Over time, this could become an important channel to air concerns, monitor and support progress and build trust on both sides," she said.
The US has been represented by a lower-ranking diplomat as a protest since Burma's military rulers refused to accept the results of the 1990 elections widely estimated to have been won by Ms Suu Kyi's party.
Mrs Clinton and Ms Suu Kyi had a private dinner in Rangoon before holding a more formal meeting at Ms Suu Kyi's residence on Friday.
It is the first time the pair have met in person. Mrs Clinton has often referred to Aung Sang Suu Kyi as a personal inspiration.
Ms Suu Kyi's National League for Democracy recently re-registered as a political party, and she is expected to stand for parliament in forthcoming by-elections.
The NLD had operated outside the political system for two decades, and Ms Suu Kyi spent much of that time in detention. She was freed shortly after the current government came to power.
During her trip, Mrs Clinton also:
- urged Burma to cut "illicit ties" with North Korea and said the regime had given assurances it was not co-operating with Pyongyang
- urged Burma to end ethnic violence and put a stop to "some of the world's longest-running internal conflicts"
- said the US would open talks with Burma to start joint searches for the remains of troops killed in World War II
- passed on a personal letter from US President Barack Obama to President Thein Sein on the new phase in relations in return for democratic reforms. In it, Mr Obama says Burma has taken some encouraging steps towards reform, but still has much to do
President Thein Sein hailed a "new chapter" in relations during talks with Mrs Clinton - the most senior US official to visit Burma in more than half a century.
Mrs Clinton's talks with Burma's leadership got under way on Thursday when she met Foreign Minister Wunna Maung Lwin before the talks with President Thein Sein.
"I am here today because President Obama and myself are encouraged by the steps that you and your government have taken to provide for your people," Mrs Clinton told Thein Sein as the two sat down for talks.
Thein Sein said her visit would prove to be a "milestone".
"Your excellency's visit will be historic and a new chapter in relations," he said before the start of the closed-door meeting.
BBC state department correspondent Kim Ghattas, travelling with Mrs Clinton, says the top US diplomat's visit is both a reward for the reforms that have already taken place and an incentive for Burma's government to do more.
The US secretary of state said before the trip she was quite hopeful that "flickers of progress" could transform into a real movement for change.
Mrs Clinton is the first secretary of state to visit Burma since John Foster Dulles in 1955.
The country was taken over by the military in 1962 and ruled by a brutal and unpredictable junta until last year, when the army ceded power to a nominally civilian government.
Although the government is still dominated by figures from the previous military regime, it has introduced several important reforms, and released groups of political prisoners.
The visit comes weeks after President Obama toured Asia and made a series of announcements bolstering American commitments in the region.
Observers have portrayed the new US focus on Asia as an attempt to counter China's attempts to become the pre-eminent power in the area.
And Chinese state media has reacted furiously to Mrs Clinton's visit to Burma.
The Global Times, which often runs bombastic nationalistic editorials, warned the US not to impinge on China's interests.
"China has no resistance toward Myanmar [Burma] seeking improved relationship with the West, but it will not accept this while seeing its interests stamped on," said a comment piece in the paper.
China has invested heavily in Burma, particularly in the energy sector.
But big Chinese-funded projects such as a hydroelectric dam in the north have provoked resentment among Burmese and led to an upsurge in fighting between ethnic rebels and the army.