"I would urge the parties to the six-party talks not to slow their efforts but to persevere and press ahead strategically to get everybody back to the table to continue discussion," Annan told reporters after meeting South Korean Foreign Minister Ban Ki-moon.
The nuclear talks have been stalled since November because of a dispute between North Korea and the United States over financial sanctions imposed by Washington for alleged illegal activities by the communist country, such as counterfeiting.
The North has refused to return to the disarmament talks, which also involve China, Japan, Russia and South Korea, until the United States lifts the sanctions.
Washington says North Korea should return to the talks without conditions and has increasingly pressured the North over its poor human rights record — a move analysts say may be aimed at pushing it to resume the nuclear negotiations.
"The nuclear issue is by far the most important and should be given a separate category and priority as compared with human rights and other activities," Annan said Monday.
Annan, who arrived in Seoul as part of a regional tour, also urged Iran "to cooperate with other European countries to find a solution" to the dispute over its nuclear program.
European Union nations are trying to persuade Iran to accept international oversight of its civilian nuclear program to make sure it is not used to produce weapons. Tehran has repeatedly asserted its nuclear program is aimed at generating power.
"Until recently we were focused on North Korea. Today we also have Iran," Annan said. "The international community has to take very urgent steps to deal with these issues."
Foreign Minister Ban said the six-nation talks remain the best forum for resolving the North Korea nuclear issue.
"We still have this principle that the North Korea nuclear issue should be resolved through resumption of the six-party talks," Ban told reporters. "Involved countries need to continue their efforts in this direction."
GlobalSecurity.org, a U.S. organization providing information about defense, intelligence and space, released satellite pictures over the weekend which it said indicated the North may have restarted its main nuclear reactor in Yongbyon, 80 kilometers (50 miles) north of the capital, Pyongyang.
Last year, the North said it had halted operations at the Yongbyon reactor and removed 8,000 spent nuclear fuel rods — a move that could allow it to harvest weapons-grade plutonium.
The pictures taken in January showed some increased activity around the reactor — more vehicles and containers as well as steam coming out of one of the towers. "The steam plume in the January 5, 2006, view is indicative of the reactor being active," the caption for one of the photographs said.
The pictures also showed that a dirt path at the facility had been paved, it said.
Annan's three-day trip to South Korea comes as Ban seeks to succeed him as head of the United Nations. Annan's second five-year term ends Dec. 31.
Annan is to leave for Tokyo on Tuesday.