North Korea "would move promptly," Richardson told a news conference in Seoul after a four-day trip to the North.
"Within a day after receiving the funds, and therefore within that day, (North Korea says it will) invite the (International Atomic Energy Agency) to Pyongyang and inspectors to draw up the terms for shutting down the Yongbyon reactor," he said.
Richardson said the North Koreans had asked for a month to complete the reactor shutdown, but that the U.S. delegation had said that was too long.
"We let them know that this was not acceptable and the issue was dropped," he said. Instead, Richardson said the shutdown should only take a "few days."
The comments were the clearest North Korean reaction yet to an announcement that authorities have released North Korea's money held in Banco Delta Asia — a Macau bank blacklisted by Washington — and raised hope for the implementation of a landmark Feb. 13 agreement in which Pyongyang promised to shut its main nuclear reactor by Saturday.
U.S. Assistant Secretary of State Christopher Hill, the main U.S. envoy to the North Korea nuclear talks, said Wednesday he hoped that U.N. inspectors would be able to travel to the North "in a matter of days."
"We see no reason why (North Korea) should hold up anything right now," Hill said in Seoul after meeting South Korean diplomats. "I don't want to get into extending the deadline."
Authorities in the Chinese territory of Macau said Wednesday that North Korea can withdraw the money.
Richardson said the Macau bank is expected to formally notify North Korea later Wednesday or Thursday that the regime can access its funds.
"So the (financial) issue is resolved and now we need to move forward," Richardson said. "Now the ball is in North Korea's court to take the next important steps."
Acknowledging it might be difficult to meet the Saturday reactor shutdown deadline, he called on the North to show goodwill by inviting U.N. inspectors by then "to at least start the process of shutting it down."
The financial issue has brought the nuclear negotiations to a standstill as North Korea insisted it would not talk about disarmament measures until it gets its money back. Pyongyang has claimed that the freeze on its funds shows the United States' hostile intentions toward the isolated communist regime.
The U.S. blacklisted the Macau bank in 2005 for its alleged complicity in counterfeiting and money laundering by North Korea. The move prompted the North to boycott the nuclear talks for more than a year, during which it conducted its first-ever nuclear weapons test in October.
Richardson said the bipartisan U.S. delegation stressed during their visit that Americans were united in seeking an end to Pyongyang's nuclear program.
"We impressed upon the North Koreans that the American people are united in seeking a peaceful and final end to North Korea's nuclear program," Richardson said.