BEIRUT (Reuters) - International mediator Lakhdar Brahimi said on Wednesday that Syria's civil war risked spreading across borders into an "all-consuming" conflict unless it was eventually addressed.

Brahimi, speaking after talks in Beirut, said he hoped this month's Islamic holiday of Eid al-Adha offered a chance for both sides to cease fire and warned that the Middle East would suffer unless the violence was contained.

"This crisis cannot remain within Syrian borders indefinitely. Either it will be addressed or it will increase ... and be all-consuming," he said.

Brahimi has visited Sunni Muslim states which support rebels fighting President Bashar al-Assad as well as Shi'ite Iran, Assad's strongest regional ally, in his search for a political solution to Syria's civil war

On Sunday he appealed to Iranian leaders to support a proposal for a ceasefire to mark Eid al-Adha. Speaking in Lebanon he said Syria's opposition had told him that any ceasefire by Assad's forces would be reciprocated immediately.

"We heard from everyone we met in the opposition, and everyone (else) we met that, if the government stops using violence 'We will respond to this directly'," he told reporters.

"We hope this will be a very small step that would save the Syrian people (the bloodshed) they are going through, because they are burying hundreds of people every day," he added.

Activists say more than 30,000 people have been killed in the fighting in Syria since the uprising against Assad's rule erupted in March last year. An April ceasefire brokered by Brahimi's predecessor, Kofi Annan, broke down within days as both rebel and government forces escalated their conflict.

"If the number of people buried during the Eid was reduced, perhaps this could be a start to bringing Syria back from the dangerous situation which it has slipped into... and we could talk to the parties inside and outside (Syria) to work towards helping the Syrian solving their problem," Brahimi said.

(Reporting by Laila Bassam; Writing by Dominic Evans; Editing by Jon Boyle)