President Barack Obama has praised Burmese President Thein Sein for his leadership in moving his country towards political and economic reform.
He was speaking after Thein Sein became the first Burmese leader to visit the White House since 1966.
For the first time, Mr Obama called the country Myanmar, the name adopted by its military rulers in 1989.
However, the US president expressed "deep concern" at violence against the Muslim ethnic minority in Burma.
Mr Obama said the US appreciated the Burmese leader's efforts "in leading Myanmar in a new direction".
"We want you to know that the United States will make every effort to assist you on what I know is a long, and sometimes difficult but ultimately correct path to follow," he said.
Mr Obama said he recognised Thein Sein had made "genuine efforts" to resolve the long-standing ethnic tensions in the country, but went on to say: "The displacement of people, the violence directed towards them needs to stop."
Thein Sein, through a translator, acknowledged Burma had "many challenges", saying that "for democracy to flourish... we will have to move forward, and we will have to undertake political reforms and economic reforms".
Speaking later at Johns Hopkins university in Washington, Thein Sein said: "Periods of transition are always fraught with risk. But I know my country and my people."
"I know how much people want to see democracy take root," he said. He also said that Burma must "forge a new and more inclusive national identity".
Referring to the recent anti-Muslim violence in Burma, he said: "We must end all forms of discrimination and ensure not only that intercommunal violence is brought to a halt, but that all perpetrators are brought to justice."
International groups have voiced concerns about serious anti-Muslim violence in Burma in recent months.
At least 40 people were killed in violence in central Burma last month, while widespread unrest in 2012 between Buddhists and Muslims in Rakhine state left nearly 200 people dead, and tens of thousands of Rohingya Muslims displaced.
Human rights groups have accused Mr Obama of moving too quickly to rehabilitate Burma as it emerges from decades of military rule.
Republican Senator Marco Rubio said that Mr Obama was too quick to reward Burma, and that "the jury is still out" on Burma's reforms.
"When rewards continue [without] progress, it undermines the ultimate success of the effort and sends the wrong message to the Burmese people about American intentions," he said.
The US leader had clearly been conscious of the criticism about the visit and the White House encounter was cordial but not effusive, reports the BBC's Paul Adams from Washington.
But the fact that it happened at all is significant and suggests that Mr Obama still regards Burma as a success story - albeit one that needs careful attention, our correspondent adds.
The US has hailed changes in the ex-military state, including the release of dissidents and relaxed censorship, since it ended almost 50 years of military rule in 2011 by establishing a nominally civilian government.
Thein Sein heads an administration that was elected in November 2010 in the country's first elections in two decades. The Aung San Suu Kyi-led opposition has a small presence in parliament after a landslide win in by-elections in April 2012 largely deemed free and fair.
Whitehouse spokesman Jay Carney said the US was using Burma's official name, Myanmar, more frequently "as a courtesy in appropriate settings".