"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 February 13 agreement," Hill said after the eight-hour meeting with Kim.
North Korea agreed to shut down its main nuclear reactor and invite back international inspectors within 60 days of the February 13 six-nation nuclear pact.
The landmark bilateral talks over two days in New York kicked off discussions to end more than 50 years of feuding between Washington and North Korea and smoothen the implementation of the nuclear accord.
Hill said they had discussed North Korea's presence on the US list of state sponsors of terrorism as well as on establishing diplomatic ties.
"We are committed to working towards that goal," he added.
He ruled out the possibility of both countries establishing liaison offices in each other's capitals as a prelude to full diplomatic ties although he said China was keen on such a model.
"I think they [North Korea] would like to move to diplomatic relations but I must say that this is very much linked to the question of denuclearisation," said Hill.
Hill had earlier said North Korea should make a full declaration of its nuclear activities including a highly-enriched uranium programme the US suspects it has.
He repeated US assertions that Pyongyang is trying to enrich uranium, allegations that has caused considerable debate in Washington after US 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 programme," Hill said.
Separately on Tuesday, the US State Department accused North Korea of continuing serious abuses against its citizens, according to its annual global human rights report.
The report said Kim Jong-il, North Korea's leader, exerted absolute rule over North Koreans already living in a repressive environment with reports of murder, disappearances and arbitrary detention by officials.
Harsh prison conditions and torture were common, and pregnant female prisoners reportedly were forced to have abortions, the report said.
"Citizens were denied freedom of speech, the press, assembly and association, and the government attempted to control all information," it added.