Hamas defeated the Fatah movement of internationally backed Palestinian President Mahmoud Abbas in 2006 parliamentary elections. After the vote, Israel began arresting Hamas legislators in the West Bank and east Jerusalem.
Hamas says 17 of the movement's 45 West Bank legislators are currently in prison. Dweik previously served 33 months of a three-year sentence for belonging to Hamas, considered a terror organization by Israel and the West.
The Palestinian parliament stopped functioning after Hamas seized Gaza from Abbas in 2007.
Also Thursday, the Israeli military announced ahead of the Muslim holy month of Ramadan steps to ease the lives of Palestinians living under restrictions in the West Bank territory it captured in the 1967 war.
Among the measures: a removal of several West Bank roadblocks, approval of thousands of permits for Palestinian constructions workers to enter Israel, and the easing of money transfers used to pay Palestinian salaries.
Palestinians over the age of 40 will also be permitted to freely enter the Temple Mount in Jerusalem for prayers during Ramadan.
Muslims believe God revealed the first verses of their holy book, the Quran, to his Prophet Muhammad during Ramadan. Devout Muslims refrain from eating or drinking during the day hours throughout the month.