US President George W Bush and his Chinese counterpart, Jiang Zemin, have said they both oppose any nuclear weapons on the Korean peninsula.

The two presidents, meeting at Mr Bush's Texas ranch, vowed to seek a peaceful resolution to the crisis that has followed North Korea's admission that it is developing nuclear arms.

It was announced after the meeting that Vice-President Dick Cheney would visit China next year.

There must be consequences (for Iraq). Let me put it bluntly: There must be consequences

George W Bush

Mr Bush said he had also urged Mr Jiang to support a tough new UN resolution on disarming Iraq.

Mr Bush said he wanted to work with China, South Korea, Japan and Russia to ''come up with a common strategy to convince (North Korean President) Kim Jong-il to disarm''.

Mr Jiang said that China had ''all along been a supporter of a nuclear-free Korean peninsula and wants peace and stability there''.

No response

However, there was less agreement on the question of Iraq.

Mr Bush said China should ''support a new Security Council resolution demanding Iraq fully disarm itself of weapons of mass destruction''.

However, Mr Jiang did not say what his response had been.

The Bush administration wants a UN resolution that carries the threat of military action unless President Saddam Hussein disarms.

Mr Jiang arrived 30 minutes late at the ranch

China, Russia and France are cool to such language.

But Mr Bush said again that he would not accept a weak resolution.

''There must be consequences. Let me put it bluntly: There must be consequences,'' he said.

The BBC's Justin Webb, who is in Crawford, Texas, said that although the vice-president's visit was the only concrete announcement, the meeting was a sign of faith that the US and China genuinely wanted a rapprochement after 18 months of difficulties.

The summit was initially arranged as a farewell for Mr Jiang, who is scheduled to leave office soon, but was changed by the fast-moving events in North Korea.

Human rights

Mr Jiang said he and Mr Bush also discussed the subject of Taiwan, and had a ''frank exchange of views''.

China regards Taiwan as a renegade province that should be reunited with the mainland, while the United States wants China and Taiwan to settle their differences peacefully.

On another sensitive issue - human rights - Mr Bush expressed his views ''on the importance of China freeing prisoners of conscience and giving fair treatment to peoples of faith''.

Harmony but not sameness, reserving differences without coming into conflict

Jiang Zemin

Mr Jiang's meeting with Mr Bush was being portrayed in Beijing as crowning his term in power.

Chinese officials were anxious that everything should go smoothly, although Mr Jiang and his wife, Wang Yeping, kept Mr Bush waiting by arriving 30 minutes late at the ranch.

Following the meeting, the two men were to join their wives for a Texan barbecue.

On the eve of the meeting, Mr Jiang had called for greater co-operation between China and the US, saying working together would benefit both countries.

He made the upbeat comments in a speech to the Texas A&M University, where Mr Bush's father - former President George Bush - was among the audience.

Apec date

But Mr Jiang also indicated that China would not fall in step with the US on everything.

"Confucius said more than 2,000 years ago: 'In human relationships, a gentleman seeks harmony but not uniformity'.

"That is to say, harmony but not sameness, reserving differences without coming into conflict."

The two presidents will now travel to Mexico for an Asia-Pacific Economic Co-operation (Apec) forum meeting.