(Adds quotes from Hill, details)

By Paul Eckert, Asia Correspondent

NEW YORK, March 6 (Reuters) - The United States said it had "very good" talks with North Korea on Tuesday and it appeared that a deal on ending North Korea's nuclear ambitions was on track for now.

Senior officials from the two countries met in New York for two days of discussions focusing on the political and legal obstacles to the normalization of ties between countries that have been bitter foes since the 1950-1953 Korean War.

The talks were called for under a Feb. 13 agreement under which North agreed to take steps to end its nuclear ambitions in exchange for aid and the prospect of other benefits.

"These were very good discussions," U.S. Assistant Secretary of State Christopher Hill told reporters after about eight hours of talks with North Korean negotiator Kim Gye-gwan. "For now we feel we are on the right track."

South Korea's Yonhap news agency quoted Kim as saying the the sessions were "constructive and sincere."

Hill said the two sides had in-depth talks on North Korea's presence on the U.S. list of state sponsors of terrorism as well as on the establishing diplomatic ties, saying: "We are committed to working towards that goal."

He was also upbeat that North Korea would meet its initial obligations under the Feb. 13 deal, which include shutting down the nuclear reactor at the the center of its atomic program and inviting back international inspectors within 60 days.

"I would say there was a sense of optimism (on) both sides that we will get through this 60-day period and we will achieve all of our objectives that are set out in the Feb. 13 agreement." Hill said.

Under the agreement, reached in talks among the two Koreas, China, Japan, Russia and the United States, the other parties agreed to give North Korea emergency energy aid equal to 50,000 tonnes of heavy fuel oil within 60 days.

It also called on North Korea to begin talks within 60 days to produce a comprehensive list of its nuclear activities.

In a speech earlier in the day at the Japan Society in New York, Hill stressed the importance of North Korea making a full declaration of its nuclear activities, including a highly enriched uranium program the United States believes it has.

VIDEO GAME CHALLENGE

In the speech, Hill repeated U.S. assertions that Pyongyang is trying to enrich uranium -- allegations that caused a 1994 U.S.-North Korea nuclear agreement to unravel and over which there is debate in Washington after U.S. officials acknowledged some gaps in intelligence.

"There's a whole list of things that North Korea has been purchasing over the years that are entirely consistent with a highly enriched uranium program," Hill said.

"If they don't have a highly enriched uranium program, why did they buy all this stuff?" he asked, referring to expensive centrifuges, aluminum tubing and manuals. He later said that he discussed the uranium issue at length with Kim in the talks.

South Korea's Chosun Ilbo daily reported that Kim had told former U.S. ambassador to South Korea Donald Gregg at a seminar on Monday that "We will act transparently on all our nuclear programs including HEU (highly enriched uranium).""

Uranium enrichment would be a second way to increase the stockpile of fissile material of North Korea, which last October tested a nuclear device made from plutonium produced by a reactor to be shuttered under the Feb. 13 disarmament deal.

The talks in New York marked the highest-level meeting between the two countries on U.S. soil since communist North Korea's leader, Kim Jong-il, sent a top envoy to Washington in 2000 in an abortive effort to improve relations.

Analysts have been skeptical about rapprochement between the United States and North Korea -- a country President George W. Bush in 2002 labeled part of an "axis of evil."

Hill struck a note of caution, saying: "This process that we're on is not unlike a video game: It gets more and more and more difficult as you go on to more and more levels."

Before the next round of six-party nuclear talks in Beijing on March 19, North Korea will hold talks with Japan in Hanoi starting on Wednesday. The parties will also have separate meetings on energy aid, the denuclearization of the Korean Peninsula and regional security next week. (Addiional reporting by Arshad Mohammed in Wshington)

(Editing by Cynthia Osterman; Reuters Messaging: paul.eckert.reuters.com@reuters.net; e-mail: paul.eckert@reuters.com; Tel: +1 202-789-8578))

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