Top negotiators of the United States and the Democratic People's Republic of Korea (DPRK) on Saturday both gave positive assessment on their bilateral talks being held here.

"All in all we had a very substantive discussion today, one of the most substantive we have had," U.S. Assistant Secretary of State Christopher Hill told reporters following the conclusion of the first day of talks.

Hill said he and DPRK Vice Foreign Minister Kim Kye-gwan discussed issues on bilateral relations and other ones related to the six-party nuclear talks.

"We do have a long way to go on many of these issues but I think we reached substantial understanding between the two of us on what needs to be accomplished in the months ahead," Hill said outside the U.S. mission to the United Nations in Geneva, where the first day of talks were held.

The two sides will continue discussions over dinner in the evening and early Sunday morning in the DPRK mission, he added.

Meanwhile, DPRK's top negotiator Kim Kye-Gwan also spoke positively about the first day of talks.

"The meeting went well today," Kim told reporters upon return to his hotel.

Kim said the two sides discussed the issue of removing DPRK from a U.S. list of so-called state sponsors for terrorism.

They also discussed how to implement the next steps concerning the denuclerization process on the Korean Peninsula.

"Both sides see their obligations ... and I expect this (two-day) meeting will have a fruitful result," Kim said.

The bilateral working group meeting is being held under a six-party agreement reached in Beijing on Feb. 13., in which the DPRK pledged to dismantle its nuclear facilities in return for aid and security and diplomatic guarantees, including normalizing ties with the United States.

Besides the United States and the DPRK, the six parties also include China, the Republic of Korea, Japan and Russia.

The DPRK has shut down a key nuclear reactor in Yongbyon according to the Feb. 13 agreement.

But the United States insists that the DPRK must completely declare and disable its nuclear arsenal before any establishment of ties between the two countries that have been enemies for over 50 years.

Hill said the shutdown of the Yongbyon reactor was phase one of the denuclerization process, while phase two will be "the disablement of the nuclear facilities and the full declaration of all nuclear programs and facilities and materials that the DPRK has."

"This next phase, which has to do with disablement and declaration on the DPRK side and economic and energy assistance and some bilateral considerations on our part, is of course a very critical phase," Hill told reporters.

Hill said the two sides discussed this next phase on Saturday and they had "an understanding on the way forward."

He also expressed hope a "February-like agreement" could be reached when the next round of six-party talks resume in Beijing in mid-September.