Asian and Pacific leaders have ended a summit in Bangkok calling for increased measures to stop the spread of terrorism and weapons of mass destruction.
The summit ended with a traditional display of finery
The meeting's chairman, Thai Prime Minister Thaksin Shinawatra, also pressed for further talks involving North Korea and the United States, calling on both sides to resolve the nuclear stand-off through dialogue.
The Asia-Pacific Economic Co-operation (Apec) meeting stressed its economic heritage by calling for increased trade liberalisation and a new impetus for trade talks which stalled in Mexico last month.
But the summit was overshadowed by US concerns about regional security, and North Korea's reported test-firing of at least one short-range missile.
Unconfirmed reports on Tuesday suggested the North might have fired a second surface-to-ship missile into the sea between the Korean peninsula and Japan, after a similar test on Monday.
Mr Thaksin said dialogue should address "all the concerns of the parties including the
security concerns raised by [North Korea]", referring to US hints it might be prepared to offer North Korea guarantees it would not be attacked.
Mr Bush, who left Thailand for Singapore on the fourth leg of a six-nation Asian tour, has sounded upbeat on the subject, saying that "we're making good progress on peacefully solving the issue with North Korea".
The statement followed earlier remarks in which he ruled out the formal non-aggression treaty with the North that Pyongyang has demanded, but hinted that there might be room for some other form of written security pledge.
However, optimism about the chance of fresh talks was overshadowed by reports that Pyongyang had test-fired another short-range missile on Tuesday.
Japanese officials said that the launches posed no immediate threat to neighbouring countries as the missiles only had a range of up to 100 kilometres (62 miles).
It was believed that any missiles had landed in the sea between the Korean peninsula and Japan.
However, South Korea's Joint Chiefs of Staff said it did not believe any missile had been fired by the North on Tuesday.
"Our system did not spot any missile launch today by North
Korea," a South Korean spokesman told Reuters news agency.
At the Apec summit, the US emphasis on the fight against terrorism has upset some delegates, who believe the organisation should stick to its stated mission of promoting free trade.
Malaysian Prime Minister Dr Mahathir Mohamad said Apec was set up as an economic and trade body and should not be dominated by security issues.
But the US insisted that terror was threatening regional economies.
"Every nation, every economy represented here, every business, every leader, every one of us is a potential target for terrorist activities," US Secretary of State Colin Powell said.