Lebanon on Friday urged the United Nations to urgently consider "alternative means" to fund a UN-backed court on its ex-premier Rafic Hariri's murder that may close over a cash crunch.

"Taking into account the ongoing acute crises that Lebanon suffers from... (we) would be grateful to Your Excellency for urgently exploring different and alternative means of financing" the Special Tribunal for Lebanon, caretaker prime minister Hassan Diab wrote in a letter to UN chief Antonio Guterres.

The STL, set up to try suspects in the 2005 killing of Hariri, said this week it risks closure by the end of July without a cash injection.

The court based in the Netherlands on Thursday cancelled the opening of a new trial of a convicted suspect that had been set for June 16 "due to lack of funds".

The STL is estimated to have cost between $600 million and $1 billion since it opened in 2009.

It draws 51 percent of its budget from donor countries and the rest from Lebanon, which is grappling with its deepest economic crisis since the 1975-1990 civil war.

The World Bank said this week that Lebanon's financial downturn is likely to rank among the world's worst since the mid-19th century.

In his appeal, Diab called on UN member states to keep the court alive.

"The most painful consequences of the cessation of the STL's work lie in the reflection of a fragmented and incomplete justice," he said.

Killed twice

Sunni billionaire Hariri, who had stepped down as Lebanon's prime minister in October 2004, was killed in a February 2005 suicide blast targeting his armoured convoy.

The attack in Beirut also killed 21 other people and injured 226.

Born from a United Nations Security Council resolution, the STL last year sentenced Hezbollah suspect Salim Ayyash in absentia to life imprisonment over the 2005 truck bombing.

The tribunal was meant to begin next week another trial for Ayyash, who remains on the run, in a separate case over three attacks targeting Lebanese politicians between 2004 and 2005.

Responding to news of the trial's cancellation, the families of victims who died in the attacks warned against impunity from justice.

"We are killed twice: first, through assassination... and then as a result of the deliberate assassination of the trial," said a woman speaking on behalf of the Hawi family at a joint news conference.

"If the court closes its doors, the family of martyr George Hawi will sue every official either in the tribunal or in the United Nations who caused delays in our case," she said.