Palestinian politicians have rejected conditions imposed by Israel on Palestinian campaigning in occupied East Jerusalem.
Israel has softened its curbs on campaigning in East Jerusalem
Earlier on Monday Israel said it would allow campaigning in East Jerusalem for the poll on 25 January, as long as they got approval from Israeli police.
Hamas members will remain barred from campaigning there, the decision said.
Palestinian leader Mahmoud Abbas has said he will postpone the polls if East Jerusalem is not allowed to vote.
And Israel had also warned it would ban Palestinians in East Jerusalem from voting if Hamas took part in the poll.
Last week, Israeli police stopped Palestinian candidates from campaigning in the area.
No specific Israeli decision has been taken on whether the vote will be allowed.
A Hamas official has said that the organisation has started campaigning in East Jerusalem.
"This is an internal Palestinian decision and internal Palestinian issue, so we've already started our campaign in East Jerusalem, and if Israeli forces want to stop some means of campaigning, we have alternative means and we can use them in our campaigning," Ziad Dayeh, the campaign manager for Hamas told BBC World TV.
The governing Fatah party's candidate in East Jerusalem, Hatim Abdelqadir, described the conditions as unjust.
An independent, Hanan Ashrawi - who had been prevented from campaigning last week - also rejected them. She demanded a clear statement from Israel on whether it would carry out its threat to bar Palestinians from voting in East Jerusalem.
Another independent, Mustapha Barghouti, said the announcement was a mere public relations exercise.
Israeli Internal Security Minister Gideon Ezra said those who wished to campaign in Jerusalem would have to get clearance from the police.
"Anyone who is a supporter of Hamas will not receive permission," he told Israel Radio.
He did not say whether residents of the area will be allowed to vote in the polls.
Israel had earlier said it would ban East Jerusalem residents from voting in protest at the participation in the election of Hamas, the largest and most popular Palestinian militant group.
However, Israeli opposition softened late last month with top officials saying they did not want Mr Abbas to blame them for sabotaging the election.
The move to partially lift curbs on campaigning is a significant one by acting Prime Minister Ehud Olmert, who assumed power when Israeli leader Ariel Sharon was taken ill last week. Mr Sharon had put off the decision on Palestinian campaigning and voting in East Jerusalem.
The 200,000-odd Palestinians living in the eastern part of East Jerusalem, occupied by Israel since 1967, were allowed to vote in an election in 1996, in which Hamas did not take part.