(Adds Nkunda threat, comments from EU's Michel and MONUC)

By Yves Boussen

GOMA, Congo, Oct 30 (Reuters) - Congolese rebel leader Laurent Nkunda threatened on Thursday to occupy an eastern city unless U.N. peacekeepers guaranteed a ceasefire, while foreign envoys scrambled to secure peace on the Rwanda-Congo border.

The threat followed a four-day offensive by Nkunda's Tutsi rebels that sent tens of thousands of civilians fleeing in Democratic Republic of Congo's North Kivu province, raising fears of a repeat of a 1998-2003 war in the African state.

Nkunda, who declared a ceasefire late on Wednesday after his forces advanced almost to the limits of the provincial capital Goma, said U.N. soldiers failed to stop civilians there being killed and robbed overnight by government troops in retreat.

"We will go into Goma if there is no ceasefire, no security and no advance in the peace process," he told Reuters by satellite phone. He said he was talking from his headquarters at Kirolirwe, in eastern Congo.

Nkunda, who has said he is fighting to protect the ethnic Tutsi minority in eastern Congo, rejected any return to a broad peace deal signed in January in North Kivu, saying the process was too dominated by President Joseph Kabila's government.

He said he was ready to talk peace, but with a neutral mediator.

As tension persisted in Goma, the United Nations, the European Union and the United States lobbied Rwanda and Congo to end the rebellion on their common border, with EU presidency holder France pressing for deployment of an EU force.

Several people were killed in looting overnight as gunfire rang out across the provincial capital and artillery boomed by the nearby border. Shooting subsided in the early hours.

MONUC spokesman Kevin Kennedy said that while the ceasefire was holding in North Kivu, the Congolese army were "running amok" in parts of Goma.

MONUC was redeploying peacekeepers from its overall 17,000-strong force in Congo -- the largest of its kind in the world -- to reinforce some 850 troops in Goma.

"We are talking about a mission that is absolutely stretched to the limit," Kennedy said.

Rwanda and Congo each accuse the other of border incursions but both deny entering each other's territory.

DIPLOMATIC PRESSURE

EU foreign policy chief Javier Solana spoke with Rwandan President Paul Kagame, while EU Aid Commissioner Louis Michel met Congo's Kabila, hoping to get the two leaders to meet.

"That will no doubt help to put in place political processes which are absolutely necessary," Solana told reporters in Paris.

"We urgently need a ceasefire to stop the chaos and the suffering of the ordinary people," Michel said in a statement.

Renegade Tutsi General Nkunda and his 4,000 rebels have fought on and off since 2004 against Congo's army, which Nkunda accuses of siding with Rwandan Hutus who took part in 1994 genocide in Rwanda of Tutsis and moderate Hutus.

A January ceasefire collapsed in August.

Nkunda, whose campaign to defend Tutsi communities has widened into a broader revolt, has demanded direct talks with Kabila's government, which has in turn insisted any talks should take place in the framework of the U.N.-brokered January deal.

French Foreign Minister Bernard Kouchner, who proposed on Wednesday the EU send up to 1,500 troops, said EU members would meet by the weekend to discuss sending a humanitarian force.

A Western diplomat said on Wednesday that Germany was resisting France's plan to send troops to Congo.

U.N. Secretary-General Ban Ki-moon is sending envoys to the Rwandan and Congolese capitals. Earlier Ban said the violence was creating a "catastrophic" humanitarian crisis.

Congo's 1998-2003 war and a continuing humanitarian emergency have killed an estimated 5.4 million people.

U.S. Assistant Secretary of State for African Affairs Jendayi Frazer also was in Kinshasa to meet Kabila.

"She is there to try to promote a peaceful solution to the conflict," State Department spokesman Robert Wood said.

Asked about Congo government accusations that Rwandan troops were fighting with his rebels, Nkunda said: "There is no Rwandan army in my movement".

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