LONDON (Reuters) - Britain's Serious Fraud Office said on Wednesday it would seek the retrial of two former Barclays (>> Barclays PLC) traders after a London jury was unable to reach a verdict on whether they had been part of a conspiracy to rig global Libor interest rates.

Greek-born Stylianos Contogoulas, 44, and American Ryan Reich, 34, were left in limbo by the outcome of London's third Libor trial that began in April.

Three of their co-defendants -- Jonathan Mathew, Jay Merchant and Alex Pabon -- were found guilty and a fourth defendant in the case, Peter Johnson, pleaded guilty to one charge of conspiracy to defraud. The men will be sentenced on Thursday.

The SFO alleged the men conspired to rig dollar denominated Libor, the London interbank offered rate, which is a benchmark for around $450 trillion in financial contracts and loans worldwide, between June 2005 and September 2007.

But the 12-person jury struggled to reach a verdict on Contogoulas and Reich. It was discharged on Monday when reporting restrictions on the three guilty verdicts were lifted.

"We have asked that the Serious Fraud Office think again as to the need for another trial in this case, Charles Kuhn, a partner at law firm Hickman & Rose who represented Reich, said.

"Mr Reich was a 24-year old first-year trader when he joined Barclays Bank in 2006. He didn't have his own trading book and he made no personal profit from the conduct complained of by the SFO," he said.

"The public interest does not require the delay, expense, uncertainty and personal agony of a retrial in this case."

A lawyer for Contogoulas said he did not believe there were grounds for another trial to take place 12 years after the alleged wrongdoing had taken place.

"Needless to say our client will strenuously contest these proceedings and continues to assert his innocence of any criminality," Roland Ellis, a lawyer at Bivonas Law in London, said.

The Barclays trial brought to five the number of men convicted to date in the British part of a global investigation into allegations of financial benchmark rate rigging. Two former bankers from Dutch lender Rabobank have been convicted by a jury in the United States.

Tom Hayes, a former Tokyo-based UBS (>> UBS Group AG) and Citigroup (>> Citigroup Inc) trader, was convicted in London last August and is serving an 11-year jail sentence. But six former brokers were in January acquitted of conspiring with Hayes to rig Libor.

The SFO said it would announce a date for the retrial "in due course".

(Additional reporting by Huw Jones; Editing by Keith Weir and Jane Merriman)

By Kirstin Ridley

Stocks treated in this article : Citigroup Inc, Barclays PLC, UBS Group AG