Delegates to the six-party nuclear talks have met in Beijng for a second day.

A diplomat who attended the talks said Thursday's meeting ended with no major problems, but he did not elaborate.

The second day of talks followed a rare one-on-one session between high-level officials from Washington and Pyongyang. But no details of their discussions were released. It was also unclear whether the chief delegates of the two countries, who met in their first one-on-one talks Wednesday, were involved.

North Korea's chief delegate, Vice Foreign Minister Kim Kye-gwan, met U-S Secretary of State James Kelly in a 90-minute private session Wednesday. Neither side gave details of the meeting, but the U-S State Department later described it as "useful."

The United States wants North Korea to end ALL of its nuclear programs, including a suspected uranium-based one. North Korea denied the existence of the uranium-based program and offered to freeze its plutonium-based nuclear weapons program in return for security assurances and economic compensation.

This week's meeting is the second round of six-party talks. The first one in August ended inconclusively.