Special state security court chairman Muhammad al-Jarmuzi adjourned the trial on Saturday until 19 June
The accused are suspected of the October 2002 bombing of the French supertanker Limburg.
At a previous hearing on 7 June, just four lawyers defended the 14 defendants in court and they announced their collective withdrawal "in the absence of a minimum level of basic justice for this trial."
The defendants, accused of forming an armed group to endanger security in Yemen, face a variety of charges, principally the attack on the Limburg as it prepared to enter Ash-Shir port, off Yemen's south-eastern coast nearly two years ago.
One killed, 12 injured
One Bulgarian crew member was killed and 12 others wounded when an explosion ripped through the tanker.
Other charges include planning attacks on US ambassador Edmund Hall and other foreign missions in Sanaa, as well as attacks on Yemeni intelligence service offices and the murder of police officers.
The trial of 11 suspects charged with bombing the US destroyer Cole began last Sunday, but was immediately adjourned for one month to allow further investigations.
They are accused of involvement in the October 2000 bombing of the Cole in Aden port which left 17 US sailors dead.
The trial had been delayed by US insistence it be preceded by the arrest of all suspects in the case.