China also vociferously defended the Burma junta in UN Security Council consultations, held to discuss the release of Suu Kyi and the much criticised national election held on November 7.
Ban and Suu Kyi held their first talks by telephone, the UN said.
They "stressed the need for the Myanmar (Burma) authorities to release all remaining political prisoners as a matter of priority, so that all citizens .. are free to contribute to advancing the prospects of national reconciliation and democratic transition," a UN statement said.
The Nobel Peace Prize winning opposition leader has made the estimated 2100 political prisoners still in Burma jails her campaign priority, according to diplomats.
Forty-six nations -- European countries, the United States, Australia, Canada and New Zealand -- presented a resolution in the UN General Assembly's main human rights committee which expressed "gravest concern" at Burma's rights record and saying the November 7 election was not "free and fair".
The resolution, which highlighted political prisoners, the use of torture and inhuman treatment, child soldiers and attacks on civilians, was backed by 96 nations and opposed by 28 with 60 abstaining.
China strongly attacked the motion.
"Finger pointing does not protect human rights," China's representative told the committee meeting."
He said the resolution "does not recognise the progress that has been made," and praised the election from which Aung San Suu Kyi's party was banned and most seats went to pro-junta groups.
Russia also opposed the resolution, while Burma's ambassador Than Swe called the resolution "seriously flawed".
Suu Kyi expressed support for a visit by the secretary general's special adviser on Burma "and her desire to engage with him for pushing ahead in addressing the challenges facing the people of Myanmar," the UN statement said.
UN adviser, Vijay Nambiar, had pressed for a visit to Burma before the election, but the junta had only agreed for him to go after the vote and Nambiar turned this down, diplomats said.
Ban visited Burma last year but was not allowed to see Suu Kyi, who was released from almost two decades of detention and house arrest on Saturday.
Ban told Suu Kyi "he was encouraged by the spirit of reconciliation emanating from her statements and appeals for dialogue and compromise following her release."
The UN leader reiterated the United Nations commitment "to uphold the cause of human rights and support all efforts by the government, Daw Aung San Suu Kyi and all other stakeholders to build a united, peaceful, democratic and modern future for their country."