The Tel Aviv newspaper said Jerusalem police confiscated the Israeli identity cards of the four council members, who refuse to give up membership in the organization. Mohammed Abu Tir, Mohammed Totach, Khaled Abu Arafa and Ahmed Atoun are being given until July to get out of the country, the report said.
The council members' identity cards were lifted after The High Court of Justice ruled it would not prevent their expulsion, Haaretz said.
The four had been warned previously by Israel they must renounce their membership in Hamas or risk losing their residency rights in East Jerusalem.
Hamas, considered a terrorist organization by Israel and many other countries, won control of the Palestinian parliament in 2006 elections and took over the Gaza Strip in 2007. That has resulted in rival governments in the West Bank and Gaza.