The Palestinian legislature is expected to being debating a definition of the new post on Monday.
This will be the first vote for a Palestinian legislature since 1996.
Today the elected Palestinian legislature has no authority.
The Palestinian legislature has 88 members, but two are in Israeli prisons on charges of terrorism, which they deny.
Hamas made a commitment to him to run in the July elections for the Palestinian legislature, continuing the group's "conversion into a political party."
With Hamas now in control of the Palestinian legislature, the invitation seemed mainly symbolic.
That Palestinian legislature would also run all of their affairs - from hospitals to schools to local police.
Israel is holding about 40 members of the Palestinian legislature and cabinet.
She was later elected to the Palestinian legislature on the Hamas ticket.
Even more important, he said, the leadership was discussing the possibility of holding new elections to the Palestinian legislature on May 15.