Police detained Ali Abd al-Imam, Muhammad al-Musawi and Husain Yusuf last month for links to the website www.bahrainonline.org, which functions as an Arabic-language forum for views on a range of subjects.
The government views the site as hostile and the three have been accused of criticising the royal family, inciting hatred of the government, spreading false news and rumours that could destabilise the nation, and violating the press code.
The detainees began a hunger strike on Saturday and have been held on a 15-day detention order at a Manama police station, where they will remain for another 15 days until the prosecution extends the detention, releases them or sends them to trial.
"My clients have rejected the bail ... they have decided to stay in prison instead," lawyer Ahmad al-Arayid said of Sunday's decision by the public prosecutor to release his clients on $2652 bail each.
About 100 supporters demonstrated outside the public prosecutor's office demanding the unconditional release of the men. The prosecutor can keep detainees in custody for a maximum of 45 days, the detained Bahrainis' lawyer said.
Ali Abd al-Imam is the founder-manager of the website which has posted reports and photos of demonstrations in Bahrain.
The government banned it in 2002, but it remains easily accessible to people outside Bahrain, while those inside the tiny island country reach it through foreign-based internet service providers.
Bahrain's king, Shaikh Hamad bin Isa Al Khalifa, has taken bold steps towards democratic reform since coming to power in 1999, including reinstating parliamentary elections, pardoning political prisoners and allowing exiles to return.
But critics charge his reforms do not go far enough towards freedom of expression and democracy.