The meeting follows a bloody crackdown on pro-democracy protests in Yangon and elsewhere in the country that human rights groups say left hundreds dead, with thousands more still detained.
In the wake of the crackdown Myanmar's military rulers have been under growing international pressure to open a dialogue with the opposition.
"Until the generals' military hardware is crumbled, they won't listen to anyone"
Oomlwin, Yangon, Myanmar
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Zalmay Khalilzad, the US ambassador to the United Nations, said Thursday's meeting was "a good thing but not sufficient."
Speaking to reporters at UN headquarters in New York he said there was an urgent need to open a "full reconciliation process" and begin a transition to democracy.
Earlier this month the UN special envoy to Myanmar, Ibrahim Gambari, visited Myanmar and urged the country's military rulers to appoint an intermediary to begin talks with the opposition.
On Friday Gambari arrived in Japan on the final leg of an Asian tour hoping to drum up regional support for putting pressure on Myanmar's rulers to end their crackdown and release political prisoners, including Aung San Suu Kyi.
The opposition leader and head of the National League for Democracy has been held under house arrest for 12 of the past 18 years.
During last month's anti-government protests, she was seen briefly at the gates of her home offering prayers for Buddhist monks who were leading the protests.
She also held two rounds of talks with Gambari during his visit to Myanmar after the military crushed the protests.
The NLD won a landslide victory in national elections held in 1990, but the military refused to recognise the result.