* Speaker goes free ahead of scheduled release
* Calls for Palestinian factional unity
(Adds Dweik comments)
By Mohammed Assadi
RAMALLAH, West Bank, June 23 (Reuters) - Israel released on Tuesday the Hamas speaker of the Palestinian parliament, Aziz Dweik, who was jailed for nearly three years over his ties to the Islamist group, his lawyer said.
The release of Dweik came after the Israeli prosecutors failed to persuade a military court last week to extend his prison term, which was set to end in August.
Israel detained Dweik, 60, and dozens of other Hamas politicians in the occupied West Bank in 2006 shortly after gunmen from the Palestinian Islamist group and other militants abducted an Israeli soldier on the Gaza Strip border.
The dragnet paralysed the Palestinian Legislative Council (PLC), which had been dominated by Hamas since it beat President Mahmoud Abbas's Western-backed, secular Fatah faction in a parliamentary election earlier that year.
The Islamists accused Israel of trying to pressure them into freeing the soldier, Gilad Shalit, who remains in captivity. Hamas said 34 of its lawmakers were still in Israeli custody.
"The Palestinians should work on releasing all lawmakers in Israeli jails in order to revive parliamentary life," Dweik told reporters outside the PLC.
But Hamas and Fatah appear to be far from reconciling. The Islamists, shunned by the West for refusing coexist with the Jewish state, seized control of the Gaza Strip in 2007, prompting Abbas to dissolve the Hamas-led coalition government.
Abbas's forces, keen to prove their law-and-order mettle to international peace mediators, have since cracked down on Hamas in the West Bank. Fatah activists in Gaza have been the target of Hamas round-ups.
"I call for the release of all (political) prisoners in Gaza and the West Bank," Dweik said.
Egypt, which is trying to broker the return of Shalit to Israel, has also hosted several rounds of Palestinian factional talks, so far with no breakthroughs. The next round is set to take place on July 7.
Dweik has been touted by Hamas as a possible replacement for Abbas.
During his imprisonment, Dweik was taken several times to a hospital in Israel, suffering from blood pressure and diabetes. It is unclear if his poor health conditions contributed to his release. (Writing by Dan Williams; Editing by Samia Nakhoul (firstname.lastname@example.org; +972-2-2950430; Reuters Messaging:email@example.com))