It is Gambari's fourth trip to the Southeast Asian country since a deadly crackdown on anti-government protesters last September sparked a global outcry.
Diplomats said the envoy told them he would meet detained democracy leader Aung San Suu Kyi but did not reveal if he would hold talks with senior junta leaders.
Suu Kyi's opposition National League for Democracy hopes the visit will kick-start stalled talks between democratic forces and the military.
The United Nations-brokered talks between a junta-appointed minister, Aung Kyi, and Suu Kyi, who remains under house arrest, began in October 2007 but stopped in January after five meetings.
Ibrahim Gambari
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NLD spokesman Nyan Win said the party will also tell the U.N. envoy to urge the ruling generals to allow regular medical check ups for Suu Kyi, whose personal physician was allowed to see her Sunday.
The Nobel Peace Prize laureate, who had her last medical check up in January, has been held under house arrest for more than 12 of the last 19 years.
Nyan Win said the party will also complain to Gambari that more than 100 of its members have been arrested since the September crackdown, including recent detentions across the country.
After his arrival, Gambari met several Rangoon-based diplomats who suggested he focus on reviving the Suu Kyi-junta dialogue and the issue of political prisoners, a Western diplomat at the meeting said.
The diplomat, who spoke on condition of anonymity so as not to breach diplomatic protocol, said the release of political prisoners was key to national reconciliation.
The diplomats also told the envoy that scheduled elections in 2010 needed to be free, fair and include representatives from across Burma's political spectrum.
Gambari last visited Burma in March, a trip he described as a disappointment. Although he was allowed to meet Suu Kyi, he did not see senior junta leaders.
The military has ruled the Southeast Asian nation since 1962 and has been widely criticized for suppressing basic freedoms and human rights.
The United Nations has a poor record in Burma. Its envoys have visited the country nearly 40 times since 1990, along with other senior officials, while the U.N. General Assembly has passed numerous resolutions calling for change.
To date, the ruling generals have virtually ignored such pressure.
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