On Sunday, Gambari met General Aung Kyi, the appointed liaison minister after the UN envoy's last visit in September, and Nyan Win, the foreign affairs minister in the capital Naypyidaw.
Gambari "expects that these initial steps will lead to early initiation of dialogue aimed at accelerating inclusive national reconciliation, the restoration of democracy and the full respect for human rights," the UN office in Yangon said in a statement.
There were no further details of the meeting with Aung Kyi, a significant figure in the military government, who met Suu Kyi for 75 minutes last week.
"Mr Gambari is scheduled to meet the prime minister and other senior members of the government and leadership as well as Daw Aung San Suu Kyi and other relevant interlocutors," the statement said.
There has been no sign of any willingness by Myanmar's government to deviate from its own "seven-step path to democracy" which, so far, has resulted only in the outlines of a constitution that would enshrine military power.
The government greeted Gambari when he arrived in Yangon with state-sponsored rallies calling for "respect" from the United Nations following its decision not to renew the visa of Petrie, who did not go to Nyapyidaw with Gambari.
"Until the generals' military hardware is crumbled, they won't listen to anyone"
Oomlwin, Yangon, Myanmar
Send us your views
Petrie was there on Friday to receive criticism for issuing a statement linking Myanmar's dire economic straits to protests in September that triggered a crackdown in which official media say 10 people were killed.
Diplomats say many more probably died.
On departure, Petrie was given a letter saying the government would not renew his credentials to the country, which are due to expire soon.
Speaking to Al Jazeera after his apparent expulsion, Petrie said: "We believe that the issue of poverty is one of the critical underlying causes of suffering in this country, we the UN are here to address it."
"And we felt it was our obligation to express not only our concern with the issue but also our determination to work in this country to try and address it."
"We Respect the UN, We Respect Gambari, Respect Myanmar," state television and newspapers quoted a slogan at one rally, one of many which people say they are forced to attend, held in the Mandalay area.
Government-controlled newspapers attacked Petrie's statement in Sunday editorials.
"The statement of the UN Country Team in Myanmar absolutely ignores Myanmar's prevailing conditions, and it is, indeed, merely a groundless one," the English-language New Light of Myanmar newspaper said.
Gambari stressed on arrival for his second visit since the monk-led protests were crushed and thousands of people arrested that Ban Ki-Moon, the UN secretary general, stood behind Petrie.
"Mr Gambari conveyed the Secretary-General's support for the Country Team and the Resident Coordinator and the important work they continue to do to improve the socioeconomic and humanitarian situation," the UN office in Yangon said in a statement.
Singapore, chairman of the Association of South East Asian Nations, of which Myanmar is a member, said it was disappointed by the move against Petrie.
The United States also condemned Petrie's apparent expulsion.
It was not clear how long Gambari would remain in Myanmar but a UN statement said on Saturday he would "stay in Myanmar as long as necessary to accomplish his mission".
A spokesman for Suu Kyi's National League for Democracy (NLD), the main opposition party, said he had not been contacted by Myanmar foreign ministry officials who set Gambari's schedule and did not know whether NLD leaders could meet him.