ASMARA, Jan 19 (Reuters) - U.S. envoy Anthony Lake left Eritrea on Tuesday after his fourth attempt in as many months to end a border dispute between Eritrea and Ethiopia.

The former U.S. national security adviser held weekend talks with Ethiopian Prime Minister Meles Zenawi in Addis Ababa and then travelled to Eritrea to meet with President Isayas Afewerki on Monday, but there was no word on the progress of the talks.

``It is not the first chance for peace, it is not the last chance for peace -- the process continues,'' a senior Eritrean government official told Reuters.

Hundreds of people were killed on three fronts after the conflict erupted last May 6, until fighting subsided with the onset of the rainy season in mid-June.

Both sides have since built reinforcements of troops and artillery along their 1,000-km (625-mile) frontier and have engaged in a vicious war of words.

A previous peace initiative by the United States and Rwanda failed to resolve the dispute, after Eritrea rejected a key element calling for a withdrawal of their troops from contested territories.

The Asmara government has instead called for international monitors to police the disputed border while ownership is established and for direct talks with Ethiopia's prime minister.

But Ethiopia rejects that proposal, saying it will not open talks until Eritrea pulls back its forces.

Subsequent unsuccessful mediation efforts by the Organisation of African Unity have been based on the same plan.