Ban, currently South Korea's foreign minister, met with Hu and State Councillor Tang Jiaxuan, who was the first foreign diplomat to meet with North Korean leader Kim Jong-Il since the declared October 9 nuclear test.
The North Korean nuclear issue was discussed during the meetings, according to South Korean officials, but details were not immediately made public.
At the start of the talks, Hu congratulated Ban on his appointment as UN secretary general.
"It is the first time in 35 years that an Asian has been elected to the post," the Chinese president told Ban.
"I believe... you will be able to play a greater role in the maintenance of world peace and common development."
Ban thanked the Chinese government for supporting his candidature.
"The Chinese government offered me extensive help and support, I want to express my heartfelt gratitude," he told Hu.
"I will make my best efforts on the issue of reform of the UN and other issues concerning the UN."
Tang told Ban in the opening minutes of their meeting that "our two countries are close neighbours and have very close relations. Your election as the UN secretary general is a big event for us, not just for South Korea." "As your Chinese friends, we have great hope and expectations for you."
North Korea staged its test on the same day the Security Council voted to elect Ban as Kofi Annan's successor.
In the lead-up to his visit, officially part of Ban's tour of UN Security Council member states to express thanks for his election, both China and South Korea said Pyongyang's nuclear ambitions would be high on their agenda.
China is regarded as one of the most important players in global efforts to curtail North Korea's nuclear program as it is the isolated nation's strongest ally, its biggest provider of aid and largest trade partner.
Chinese foreign ministry spokesman Liu Jianchao emphasised on Thursday that China would focus on ways to restart the stalled six-nation talks aimed at convincing North Korea to abandon its nuclear program.
"We hope we can strengthen our co-operation with the ROK (South Korea) to promote the resumption of the six-party talks and relax the current tensions," Liu said.
The six-nation talks -- involving hosts China, the two Koreas, the United States, Japan and Russia -- have been stalled since November last year, with Pyongyang refusing to attend in protest at US financial sanctions against it.
A resumption is one element of a Security Council resolution on North Korea following its atomic test which sparked international concern.
Spokesman Liu said China hoped Ban's visit could help "achieve the objective of the denuclearization of the Korean peninsula and preserve peace and stability in Northeast Asia".
China was also hoping to have an exchange of views with Ban on China-UN relations, Liu said.
Ban said in Seoul this week he intended to play an active part in finding a peaceful settlement to the North Korean crisis.
Ban, who has spent years dealing with the North Korean nuclear issue, has promised to end a "crisis of confidence" and heal divisions hampering the work of the UN. He has also pledged to appoint a special UN envoy on North Korea when he takes over in January.
Ban is scheduled to travel to Russia and France next week.

Copyright AFP (Agence France-Presse), 2006