The decision means that nuclear inspectors, who were blocked last month from entering nuclear facilities but not removed from the country, could return to their work at the nuclear site in Yongbyon, the Los Angeles Times reported.
Surveillance cameras installed by the inspectors were expected to be turned back on Monday, and North Koreans were expected to resume the removal of fuel from a nuclear reactor.
In June, President Bush had promised to remove North Korea from the terrorism blacklist to reward the country for its denuclearization efforts, but the process stalled when North Korea would not agree to inspection and verification procedures.
North Korea then suggested it might launch another round of missiles or even conduct another nuclear test before the end of Mr. Bush's term.
U.S. Assistant Secretary of State Christopher Hill went to the capital Pyongyang for three days this month to try to work out an agreement on verification.
In a statement issued Sunday, North Korea said that because the United States had acted, it had "decided to resume the disablement of nuclear facilities in Yongbyon and allow the inspectors ... to perform their duties on the principle of 'action for action,'" according to the Times.
A fact sheet released by the State Department on Saturday said, however, that inspectors could visit undeclared nuclear sites only by "mutual consent."
Experts still predict a bumpy road ahead for North Korea's nuclear dismantlement.
Cheong Seong-chang, a North Korea expert at the Sejong Institute, a private security think tank near Seoul, said the next stage "will be more complicated," the Associated Press reported.
Cheong said North Korea could ask for increasingly difficult concessions like the normalization of diplomatic ties with the United States and the withdrawal of American troops from South Korea before it fully dismantles its nuclear facilities at Yongbyon.