About 200,000 people have signed an online petition calling for the release of BBC reporter Alan Johnston.
Alan Johnston has been held since 12 March
Mr Johnston was kidnapped in Gaza on his way home on 12 March.
On Monday, Hamas security forces in Gaza detained members of the Palestinian militant group which claims to have abducted the journalist.
Hamas seized control of the Gaza Strip three weeks ago and it has consistently called for the kidnappers of Mr Johnston to set him free.
The BBC held a rally for Mr Johnston on Monday to mark the beginning of the 16th week since his disappearance. The online petition was launched on 2 April.
Among those arrested on Monday was Khattab al-Maqdisi, a spokesman of the Army of Islam group, Hamas said.
"The arrests were carried out after all negotiation attempts... failed to free the abducted journalist," the Hamas-run interior ministry said in a statement.
"The arrests are targeting figures who were involved in the abduction of the journalist," the interior ministry statement said.
Tensions between Hamas and the Army of Islam have been growing since Hamas seized control of the Gaza Strip.
Hamas has demanded that the Army of Islam release Mr Johnston, threatening to "use all means to secure his life and to free him".