President Bush and South Korean President Roh Moo Hyun yesterday stressed their common objective of getting North Korea to return to disarmament talks, putting aside tactical differences on how hard to push the North Korean government to terminate its nuclear programs.

The two men and their top aides met for 50 minutes in the Oval Office and then held a working lunch, where they exchanged detailed -- and sometimes different -- assessments of North Korean behavior and covered a range of bilateral and regional issues, U.S. and Korean officials said. Roh told Bush that it was necessary to be firm and tough with North Korea, but it was important to resolve the impasse over North Korea's weapons through a six-nation negotiating process that has been stalled for a year, the officials said.

Stealing some of the thunder from the summit, North Korean officials met with U.S. officials on Monday and said they were committed to the talks but would not set a date for their return. Some U.S. officials have pressed to begin bringing sanctions against North Korea, such as referring the matter to the U.N. Security Council, but China and South Korea have resisted that approach.

White House spokesman Scott McClellan said Bush and Roh are "somewhat hopeful" North Korea would return to the talks, which include Japan and Russia.

The U.S.-South Korean relationship is an important domestic issue for Roh, and South Korean officials appeared eager to show that the alliance remained steady.

"There are, admittedly, many people who worry about potential discord or cacophony between the two powers of the alliance," Roh told reporters. But he said that "with regard to all the matters and all the issues of great importance, we were able to deal with them and we were able to bring closure to them smoothly."

Bush, for his part, declared "the alliance is very strong." Roh said there are "one or two minor issues" that need to be worked out. A senior South Korean official said Roh was referring to a debate over a joint military plan known as OPLAN 5029, which prepares for the collapse of North Korea. The Pentagon has had extremely difficult negotiations with South Korea over the plan, and earlier this year senior South Korean officials vetoed it, saying that giving command authority to the U.S. military would limit South Korean sovereignty.

Earlier this week, South Korean newspapers said that a senior defense official, Richard P. Lawless Jr., privately threatened while visiting Seoul to withdraw U.S. troops from the peninsula over the dispute. Bush and Roh agreed the matter should be settled by aides at lower levels, officials said.

Both sides stressed their common agreement that North Korea should give up its nuclear programs, which U.S. intelligence estimates have now produced about nine nuclear weapons.

South Korean Foreign Minister Ban Ki Moon told reporters that the two presidents "reaffirmed that no nuclear program would be tolerated." McClellan said, "We share the same goal of a denuclearized peninsula, a peninsula that is at peace."

Since the United States declared in 2002 that North Korea admitted it had a clandestine uranium enrichment program, the South Koreans and Americans have diverged over how to achieve that goal. South Korea, which retains a booming trade relationship with North Korea, has emphasized engagement and economic incentives. The United States has argued that economic incentives too soon would be succumbing to blackmail, and has pressed instead for North Korea to commit to give up its weapons first.

Ban said that, during the meetings, Bush told Roh he did not understand why North Korea was so suspicious of U.S. intentions. Pyongyang broadcast a commentary yesterday in which it said the administration's "hostile policy . . . is unprecedented in its vicious nature" but the time had come for the United States to accept the notion of "peaceful coexistence."

North Korean media recently approved of Bush's use of the honorific "Mr." when referring to North Korean leader Kim Jong Il. Bush appeared careful to use the phrase again yesterday.

North Korea has never officially responded to a U.S. proposal made at the talks last June. Under the proposal, if North Korea agrees to end its programs, South Korea and other U.S. allies could provide immediate energy assistance to North Korea. Pyongyang would have three months to disclose its programs and have its claims verified. Only then would the United States and allies give written security assurances and enter a process that might result in direct U.S. aid.

"The plan is still there, and it's full of inducements," Bush said.

In the past, South Korean officials have pressed the United States to show greater flexibility in the proposal; for example, participating in the energy assistance by paying some of the costs of administration. But Roh in yesterday's meetings with Bush did not press for greater flexibility, U.S. and Korean officials said.