The arrests, which Amnesty International denounced as a "draconian clampdown" on media freedom in Egypt, comes weeks after the arrest of two reporters on allegations of incitement to protest.
Union chief Yahiya Kallash had denounced the arrests earlier this month and told a news conference that President Abdel Fattah al-Sisi's government is "escalating the war against journalism and journalists".
Yesterday, the Cairo prosecutor summoned Kallash, union secretary general Gamal Elbashy and the head of its freedoms committee Gamal Abd el-Rahim for questioning, the latter told AFP.
The prosecutor then ordered the release of the three on condition that they post bail of 10,000 Egyptian pounds (1,000 euros, USD 1,100) each, until the outcome of the investigation.
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"We refused to pay," Abd el-Rahim said by mobile phone.
As a result they were kept in custody until a decision by the prosecutor, who could revoke the bail or remand them in custody for four days.
Amnesty's deputy director for the Middle East and North Africa, Magdalena Mughrabi, said the arrest "signals a dangerous escalation of the Egyptian authorities' draconian clampdown on freedom of expression and demonstrates the extreme measures the authorities are prepared to take in order to tighten their iron grip on power".