(in full) SEOUL (Reuters) - South Korea wants to hold talks with the United States and Japan next month to refine their policy in handling the crisis over North Korea's nuclear program, a government official told Reuters on Sunday.

"The government is pushing for the meeting sometime in June after a summit with Japan to discuss North Korean issues," a Unification Ministry official said.

He was referring to a forum involving foreign ministers of South Korea, Japan and the United States, known as the Trilateral Coordination and Oversight Group.

North Korea said late on Saturday it would agree to U.S. demands to hold multilateral talks over its nuclear program that included South Korea and Japan, but only if Pyongyang and Washington held bilateral talks first.

South Korea's presidential spokeswoman Lee Ji-hyun said the statement by the north's foreign ministry showed that Pyongyang had the "intention to talk," but nothing was firmed up yet.

A Japanese foreign ministry official in Tokyo welcomed the North Korean statement, saying it reflected Pyongyang's stance of seeking continued dialogue with countries concerned about the nuclear issue, Kyodo News Agency said.

The summit between South Korean President Roh Moo-hyun and Japanese Prime Minister Junichiro Koizumi is scheduled for June 7 in Tokyo.

On Friday, Koizumi and President Bush warned of "tougher measures" against North Korea if the communist country escalated a crisis over its nuclear weapons program.

The two leaders also said they believed a peaceful solution was possible and Bush suggested that poverty-stricken North Korea could receive "help" if it gave up its nuclear ambitions.

The nuclear crisis erupted in October when Washington said North Korea had admitted to a secret program to enrich uranium for nuclear arms, in addition to a plutonium program frozen under a 1994 U.S.-North Korea pact.