By Barnaby Mason BBC diplomatic correspondent

North Korea's renewed call on the United States to engage in direct talks without preconditions comes amid increasing efforts by several countries to resolve the crisis over Pyongyang's nuclear programme.

Each party in the diplomatic flurry sparked by Pyongyang's apparent resumption of its nuclear programme says it wants a peaceful settlement.

But no-one can quite see what an agreement would consist of or how to get there.

The South's Deputy Foreign Minister Lee Tae-shik is shuttling between the North's allies

The South Koreans are the most intimately concerned. The possibility of war is horrifying though probably still distant but they are increasingly worried about the threat of it damaging their economy.

The South Koreans are taking the diplomatic initiative - one envoy went to Beijing and another is going to Moscow to try to get the Russians to use their influence on North Korea.

Russia has criticised both the North Koreans and the Americans.

Mediation plan

Advisers to the new South Korean president who takes office next month are actually suggesting he might mediate between Pyongyang and Washington, seeking concessions from both sides.

North Korea would drop any nuclear weapons programme, while the United States would guarantee the security of the North, the plan goes.

That chimes with the North Koreans' demand for a guarantee that Washington will not use military force against them.

President Kim Dae-jung and his successor Roh Moo-hyon both back engagement

Several governments would like the Bush administration to give North Korea something, reflecting the belief that North Korea is using its nuclear weapons programme as a lever to get what it wants diplomatically from Washington - aid, recognition, direct talks.

But the Bush administration does not see why it should reward what it considers to be bad behaviour by the North Koreans.

The bottom line for President Bush is that war is not a practical option against North Korea, so pressure from other countries is the best instrument he can think of.