It is the first time Mahmoud Abbas has said he may postpone the poll.
"We all agree that Jerusalem should be included in the elections," Abbas said in Doha, Qatar, on Monday.
"If it is not included, all the factions agree there should be no elections."
Israeli officials initially said they would not allow voting in East Jerusalem - occupied and then annexed in 1967 - even via post offices as in previous ballots, but they have since indicated that they will "contemplate" allowing Palestinians to vote.
Abbas has been under pressure by senior figures of his Fatah party to delay the vote.
On Saturday, eight members of Fatah's central committee, including Ahmad Qureia, the prime minister, and Nabil Shaath, his deputy, called for the elections to be postponed.
The committee said elections would not proceed without guarantees that Palestinians in occupied East Jerusalem could vote, after holding an emergency meeting on Sunday.
Call for calm
Abbas also called on Palestinian factions to continue observing the period of calm with Israel, agreed on in February, saying that was the only way to make the Palestinian elections a success.
Abbas had earlier said: "This is only one condition, that they (the elections) proceed in Jerusalem as was the case during the legislative elections in 1996 and the presidential election in 2005.
"We all agree that Jerusalem should be included in the elections. If it is not included, all the factions agree there should be no elections"
"Nobody will accept that the Palestinians of Jerusalem will not take part in the elections of 25 January, because this is a sacred national event for us."
Fatah's traditional domination of Palestinian politics is facing an unprecedented challenge from the resistance group Hamas, which is taking part in legislative elections for the first time.
Fatah meeting stopped
Meanwhile on Monday, Israeli police broke up an "illegal" electoral meeting held by Fatah in East Jerusalem.
A police spokesman said on Monday: "The police dispersed a Fatah meeting which was being held in the Christmas Hotel.
"Officers informed the participants that the holding of this meeting was illegal and ordered them to leave."
Separately, Gideon Ezra, Israel's internal security minister, said Palestinians moving between Gaza and the West Bank should be better monitored to prevent them from smuggling arms.
In a related development, a team of European observers tasked with monitoring the Palestinian elections, have begun work in the occupied Palestinian territories.
Thirty-two of the 200 observers have begun touring the West Bank and Gaza.