They submitted an "expert report" that they said confirmed Rajab was in charge of his Twitter account where allegedly offensive tweets were posted, the source said.
The defence, for its part, reiterated it case that Rajab was not in control of his account at the time the tweets were posted.
The court had ordered the appointment of an expert from the interior ministry's cyber crimes unit to determine who was operating Rajab's Twitter account.
The hearing was adjourned to February 21.
Rajab is accused of "spreading false news and rumours and inciting propaganda during wartime which could undermine the war operations by the Bahraini armed forces and weaken the nation", according to state media.
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Sunni-ruled Bahrain is part of a Saudi-led coalition battling Shiite Huthi rebels in Yemen.
Shiite human rights activist Rajab, who had been pardoned for health reasons in 2015, was rearrested in June and is on trial on a list of charges, including insulting a state institution and Saudi Arabia in online postings.
A Bahraini court had last month ordered Rajab freed pending the trial on charges of spreading false information.
But the prosecution decided to keep Rajab in custody pending questioning in another cyber crime case on a similar charge of "spreading false news about the situation in the kingdom".
Rajab has been repeatedly detained for organising protests and publishing tweets deemed insulting to Bahrain's Sunni authorities.
He previously served two years in jail on charges of taking part in unauthorised protests in the Shiite-majority kingdom.
Home to the US Navy's Fifth Fleet, Bahrain has been rocked by unrest since security forces crushed Shiite-led protests in 2011 demanding a constitutional monarchy and an elected prime minister.