Gideon Ezra, the internal security minister, said on Monday: "It has been decided to allow electioneering in Jerusalem by candidates who do not represent groups still carrying arms, such as Hamas.
"All those who want to campaign will submit requests in advance to the Jerusalem police, and only those who don't represent extremist groups will receive permission."
Israeli police said earlier they had authorised Palestinians to campaign in annexed east Jerusalem.
Shmuel Ben Rubi, a spokesman for Jerusalem police, said on Sunday: "On orders from the political echelon, police have authorised Palestinian candidates to campaign under conditions."
However, he did not elaborate on the conditions.
Speaking from the West Bank town of Ram Allah, Hatim Abd al-Kader, a candidate for the main ruling Fatah party, confirmed that he had been informed by Israeli police officers that his faction could now campaign in east Jerusalem.
Abd al-Kader said: "I was summoned by police who told me that they had authorised Fatah to campaign in Jerusalem.
"However, they asked to be informed of electoral meetings in advance and that posters only be put up on billboards."
Police stopped two leading candidates from canvassing in the occupied Arab quarter of the city last Tuesday, on the first day of campaigning for the election, prompting fresh threats for the ballot to be delayed.
Israel is still to announce a formal decision on whether to allow Arabs to vote at post offices in east Jerusalem, as was sanctioned in a Palestinian presidential election last January and the previous legislative poll in 1996.
On Saturday, EU election monitors overseeing preparations for the election urged Israel to decide as soon as possible on the matter to allow for adequate provisions to be put in place.
Ehud Olmert held his first cabinet
meeting on Sunday
But a spokesman said the EU mission had no official contact with the Israeli government since Ariel Sharon, the Israeli prime minister, fell critically ill on Wednesday, all but paralysing the authorities from taking major policy decisions.
Ehud Olmert, acting prime minister, said after a cabinet meeting on Sunday that it was business as usual for the government.