ALSO:

Key dates in recent U.S.-North Korea nuclear talks

In this story:

• North Korea wants millions for access
• Steps toward permanent peace
• Related stories and sites

WASHINGTON (CNN) -- The United States says that North Korea brought a "problem-solving approach" to talks that concluded Monday in Geneva over a suspected nuclear construction site in North Korea.

"Differences do remain between the two sides, but we are negotiating seriously. They are bringing a problem-solving approach to this," State Department spokesman James Foley said Monday.

Foley also said that four-party talks held last week in Geneva on a permanent peace settlement to the Korean Peninsula achieved "modest, but ... significant" progress.

"For the first time since the Korean War armistice, the parties have now begun to sit down at a table and engage in substantive talks designed to take concrete steps towards establishing a new peace regime in place of the armistice, and reducing tension on the Korean Peninsula," he said.

Representatives from the United States and North Korea met over the past two weekends to try to resolve the issue of an underground complex at Kumchang-ri, near Yongbyon atomic reactor, which North Korea mothballed under a 1994 accord with Washington.

Washington has said the construction threatens the agreement, which provides North Korea with two non-military nuclear reactors and $5 billion worth of fuel oil in exchange for a commitment by the Pyongyang regime to freeze its nuclear program.

North Korea wants millions for access

The United States is demanding access to the site in order to allay its concerns that North Korea is violating the agreement to refrain from nuclear activity.

North Korea, which faces severe economic problems, has denied the site has a nuclear role and demanded compensation of $300 million if U.S. inspectors visit the site and find nothing amiss.

Foley said the United States will not pay compensation for access to the site. But he said the United States has "consistently responded favorably" to U.N. World Food Program appeals of emergency food for North Korea.

Foley said that the two sides have agreed to continue meeting over the issue, though no date or place has been set.

The U.S. Congress has given Pyongyang a de facto deadline, mandating an end to funding for fuel oil deliveries to North Korea after June 1 if the site is not opened for inspection.

The United States is concerned about North Korea's developing ballistic missile program

Along with the suspected nuclear site, the United States is concerned with North Korea's development of a ballistic missile program and its exports of military hardware to other countries.

Steps toward permanent peace

In addition to bilateral talks over the Kumchang-ri facility, teams from the United States, South and North Korea and China met last week in Geneva to try to bring a permanent peace settlement to the Korean Peninsula.

On these talks, Foley reported "modest, but in some sense significant steps" toward reducing tension between the two Koreas.

Foley said the parties held subcommittee meetings for the first time to discuss reducing tension and establishing a new peace regime between North and South Korea, which are still technically at war. The Korean War ended in 1953 with an armistice that has never been replaced with a permanent peace agreement.

CNN's Sharona Schwartz and Reuters contributed to this report.