* Three Armenian soldiers die in border incident
* War between Azeris, Armenians erupted in 1991
* Clinton urges further economic reform in Armenia (Adds details on incident in which Armenian soldiers died)
By Arshad Mohammed
YEREVAN, June 4 U.S. Secretary of State Hillary Clinton voiced concern on Monday that violence between Armenia and Azerbaijan could lead to a broader regional conflict as three Armenian soldiers died in a border incident.
Clinton began a trip to the South Caucasus region by calling on all sides to renounce violence as the former Soviet republics traded accusations over a clash that killed the Armenian soldiers and wounded troops on both sides of their border.
"I am very concerned by these incidents and have called on all parties, all actors, to refrain from the use or threat of force," Clinton told reporters at a news conference with Armenian Foreign Minister Edward Nalbandian.
"There is a danger that it could escalate into a much broader conflict that would be very tragic for everyone concerned," she added.
War between ethnic Azeris and Armenians erupted in 1991 over the mostly Armenian Nagorno-Karabakh region, which broke away from Muslim Azerbaijan with the backing of Christian Armenia as the Soviet Union collapsed two decades ago.
Sporadic violence still flares along a ceasefire line negotiated in 1994. Some 30,000 people were killed and about 1 million became refugees, the majority in Azerbaijan.
The last three years have seen skirmishes mainly on the frontline around Nagorno-Karabakh, raising fears of a return to full-blown conflict in the South Caucasus, an important route for oil and gas from the Caspian region to Europe.
The latest incident, however, took place more than 400 kms (250 miles) away from Nagorno-Karabakh.
Clinton's South Caucasus trip will focus largely on security and democratic reform in the region criss-crossed by energy pipelines, fraught with territorial disputes and the site of a five-day war between Russia and pro-western Georgia in 2008.
Clinton met Armenian President Serzh Sarksyan and Nalbandian during a roughly five-hour visit to Yerevan. Speaking in the Aremenian capital, Clinton urged Armenia and Turkey, whose border has been closed since 1993, to normalize relations.
Turkey closed its border with Armenia in a gesture of solidarity with ethnic kin in Azerbaijan during the Nagorno-Karabkah conflict.
While Armenia and Turkey signed an agreement in October 2009 to normalize relations, open the border and develop trade, tourism and economic cooperation, they never ratified the pact.
The lack of a permanent settlement to the Nagorno-Karabakh conflict, despite mediation led by France, Russia and the United States, scuttled Ankara's and Yerevan's efforts to normalise relations.
Clinton also urged Armenia, whose closed borders with Azerbaijan and Turkey make it dependent on Iran and on its former Soviet master Moscow, to pursue reforms to improve its economy as well as to strengthen democratic institutions.
"Private sector investors are looking for an open business climate with predictable rules and independent judiciary, transparent regulations, taxes and customs," she said. While Clinton said that the United States was at progress Armenia had made, she urged it to undertake more economic reform this year.
From Yerevan, Clinton flew to Georgia's Black Sea resort of Batumi where she will spend two nights before traveling to Azerbaijan, where her visit has been carefully calibrated to spend roughly the same amount of time as she did in Armenia. (Additional reporting by Margarita Antidze, Writing by Thomas Grove, Editing by Michael Roddy)