The DPP said the prosecution was an "exceptional case"
Prosecutors say they will seek a retrial of three men who had been accused of taking part in a plan to blow up transatlantic airliners.
Ibrahim Savant, 28, Arafat Khan, 28, and Waheed Zaman, 25, were found not guilty of plotting to bomb aircraft.
But jurors at Woolwich Crown Court on Monday, failed to decide whether they were guilty of conspiracy to murder.
Three other men were convicted of plotting to bomb planes flying between London to North America.
The Director of Public Prosecutions, Keir Starmer, said he had "considered very carefully" whether to seek the retrial.
He added that he had judged that "there remains a realistic prospect of a conviction against each defendant on the charge of conspiracy to murder" even though two previous juries had been unable to agree on the charge.
He added: "I have concluded that, in this exceptional case, it is in the public interest to seek a further retrial."
A judge will decide whether the men should face a third trial.
The independent reviewer of terrorism laws, Lord Carlile, said: "We have to trust judges of that seniority and quality to decide whether it is oppressive to have a third trial or whether in a case of this huge importance, it is in the public interest to see whether a jury can reach a verdict.
"It may be a verdict of guilty. It may be a verdict which may exonerate these men."
Mr Savant is from Stoke Newington, east London, and Mr Khan and Mr Zaman, are both from Walthamstow, east London.
On Monday, Abdulla Ahmed Ali, 28, of Walthamstow, Tanvir Hussain, 28, of Leyton, east London, and Assad Sarwar, 29, from High Wycombe, Buckinghamshire, were all found guilty of conspiring to activate bombs disguised as drinks.
The arrests in connection with the plot in August 2006 caused chaos to international aviation and prompted the current restrictions on bringing liquids on board aircraft.