* Fighting erupted in 1991, ceasefire brokered in 1994

* Region criss-crossed by energy pipelines

* War could draw in regional powers - think-tank

TBILISI, June 1 (Reuters) - The former Soviet republics of Armenia and Azerbaijan are closer to war over the breakaway Nagorno-Karabakh region than at any point since a ceasefire brokered more than 20 years ago, the International Crisis Group said.

Fighting between ethnic Azeris and Armenians first erupted in 1991 and a ceasefire was agreed in 1994. But Azerbaijan and Armenia have regularly traded accusations of violence around Nagorno-Karabakh and along the Azeri-Armenian border.

Clashes over control of Nagorno-Karabakh, which lies inside Azerbaijan but is controlled by ethnic Armenians, have intensified in the past three years and turned into a violent flare-up of the conflict last April, when the International Crisis Group (ICG) said at least 200 people were killed.

It said any descent into all-out war could draw in regional powers, which include Russia and Turkey - closely allied to Armenia and Azerbaijan respectively.

Since mid-January this year, deadly incidents involving the use of heavy artillery and anti-tank weapons have occurred and May saw a significant increase, including reports of self-guided rockets and missiles used near densely populated areas along the contact line.

Efforts to secure a permanent settlement of the conflict in the South Caucasus, which is criss-crossed by oil and gas pipelines, have failed despite mediation led by France, Russia and the United States, known as the OSCE Minsk Group.

“A year after Nagorno-Karabakh’s April 2016 violent flare-up, Armenia and Azerbaijan are closer to war than at any point since the 1994 ceasefire,” the ICG said in a report titled “Nagorno-Karabakh’s gathering war clouds”.

“While violence remains at a relatively low boil, any escalation quickly could spin out of control,” the think-tank, which works to prevent conflict, said.

The ICG, which based its report on the findings of analysts who had talked to residents and observers on the ground, said the settlement process had stalled, making the use of force tempting, at least for tactical purposes, and both sides appeared ready for confrontation.

“These tensions could develop into larger-scale conflict, leading to significant civilian casualties and possibly prompting the main regional powers to intervene,” the ICG said.

The ICG said that Russia remains the most influential foreign player, yet its role is complex.

“It is prima inter pares in the Minsk Group, but also chief arms supplier to Azerbaijan and Armenia, both of whom suspect Russia is more interested in expanding its influence in the region than in resolving the conflict,” the group said.

The Minsk Group is part of the efforts by the OSCE European security watchdog to find a solution to the conflict.

According to the report, Armenia – concerned about Nagorno-Karabakh’s security and angered by Baku’s increased assertiveness – insists on a lowering of security risks before substantive talks can start.

It said Azerbaijan – frustrated with the longstanding status quo and concerned that additional security measures could further cement it – insists substantive discussions cannot be delayed.

Government officials in Armenia and Azerbaijan had no immediate comments on the report. (Editing by Alison Williams)