(Adds meeting between former U.S. official and North Korean negotiator; U.S. State Department comment)
SEOUL, May 26 (Reuters) - South Korea and China agreed on Monday that recent nuclear activity by North Korea posed a serious threat to the peace and stability of the region and Pyongyang must not conduct a nuclear test, Seoul said after a meeting of their top diplomats.
Renewed activity at North Korea's nuclear test site has indicated Pyongyang may be preparing a fourth nuclear test in contravention of U.N. sanctions.
Analysis have suggested the North may be close to miniaturising a nuclear warhead to mount on a missile, alarming regional powers that have for two decades tried to rein in Pyongyang's atomic programme.
Chinese Foreign Minister Wang Yi held talks with his South Korea counterpart Yun Byung-se to discuss the North's nuclear programme, as well as an upcoming visit by Chinese President Xi Jinping to Seoul this year, South Korea's foreign ministry said.
"The two ministers agreed to step up cooperation based on the united position that they object to the North's nuclear test and that recent nuclear activities by the North pose a serious threat to the peace and stability of the Korean peninsula and the region," the ministry said.
China, North Korea's lone major ally, is usually very guarded in its opinion on Pyongyang's nuclear programme, usually expressing its desire for a nuclear-free "Korean peninsula" and careful not to be seen to be taking sides.
Wang said before his meeting with Yun that it was important for six regional partners, including the United States and North Korea, to work to resume the so-called six-party talks aimed at ending North Korea's nuclear programme.
The talks produced an agreement in 2005 to provide impoverished North Korea with aid in return for Pyongyang taking steps to suspend its nuclear programmes. But the deal was proclaimed dead in 2008 by Pyongyang and Washington.
The United States and South Korea demand the North take steps agreed in the 2005 deal as a precondition to more talks. But Pyongyang and Beijing, which has hosted the negotiations, have since sought an unconditional resumption.
Separately on Monday, a former official of the U.S. State Department, Joel Wit, confirmed he had met with North Korea's chief delegate to the six-party talks, Ri Yong-ho, but the State Department said it was a private, not an official contact.
South Korea's Yonhap news agency said the talks, which also involved a former CIA analyst, Robert Carlin, took place in the Mongolian capital of Ulan Bator on Friday.
Wit, who worked in the past on U.S. strategies to deal with North Korea's nuclear weapons programme and is now a visiting fellow at Johns Hopkins School of Advanced International Studies in Washington, confirmed to Reuters that the meeting had taken place, but declined to give details.
An official at the U.S. State Department said it had its own separate channels of communication with North Korea and no current U.S. government official had participated.
"They are acting in their private capacity," the official said. "If any former U.S. government officials choose to meet (North Korean) officials, they do so in their private capacity and will not be carrying any messages from the U.S. government."
The official said the U.S. message to North Korea was unchanged - that Washington remained committed to "authentic and credible negotiations" to implement the 2005 agreement.
"But the onus is on North Korea to take meaningful actions toward denuclearisation and refrain from provocations," he said. (Reporting by Jack Kim; Additional reporting by David Brunnstrom in Washington; Editing by Nick Macfie and Dan Grebler)