South Korean television earlier reported that North Korea destroyed the 20-meter (60-foot) cooling tower shortly after 4:00 p.m. (7:00 GMT).
"We welcome this step, and consider it one of the first real measures aimed at achieving the ultimate goal - to free the Korean peninsula of nuclear weapons," the ministry said in a statement.
Although the demolition was a rather symbolic move because North Korea switched off its 5 MW nuclear reactor at Yongbyon, about 100 km (62 miles) north of Pyongyang, last year and has already begun disabling other nuclear facilities monitored by U.S. specialists, it may still be considered as a sign that the reclusive communist regime is serious about its nuclear disarmament.
The demolition came after North Korea handed over detailed data on its nuclear activities to China Thursday, breaking a deadlock in nuclear disarmament talks with China, the U.S., South Korea, Russia and Japan.
The six-party talks stalled late last year, when Pyongyang missed a deadline to transfer nuclear data as part of a deal under which the North was promised economic aid and diplomatic incentives.
Following North Korea's declaration the U.S. announced it would lift unilateral trade sanctions against the communist country and remove it from a terrorism blacklist. U.S. President George Bush told reporters the move was "a step in the right direction," but added that Washington remained concerned about North Korea's uranium enrichment activities and suspected sales of nuclear technology to other countries.
North Korea's "nuclear declaration" also dominated the agenda of a Group of Eight (G-8) two-day meeting of foreign ministers in Japan. The G-8 top diplomats welcomed the document but stressed in a joint statement the importance of a thorough verification process under UN resolutions 1695 and 1718.
According to various estimates, Pyongyang has secretly produced about 35-50 kg of weapons-grade plutonium and shook the world in 2006 by conducting an underground nuclear test.
The test spurred the current six-party talks on North Korea's nuclear disarmament.