The delay comes as a rocket fired from the Gaza Strip hit Israel without causing casualties in the first chink in the fragile calm maintained in recent weeks.
In a move that is also likely to raise tensions, the Israeli authorities have given the green light for the construction of more than 3500 new homes in the West Bank, east of Jerusalem.
Israeli officials had said they would begin to hand over security control to the Palestinian Authority in the West Bank city of Tulkarim on Monday, less than a week after beginning a similar transfer in Jericho.
But talks on Sunday between Israeli and Palestinian officers failed to resolve all the questions.
"We didn't come to a positive conclusion and we are going to continue the discussion on Monday," the head of the Palestinian delegation, General Said Fashi, said.
An Israeli military source said they "should meet again soon" to resolve the outstanding questions.
According to a source close to the Palestinian delegation, the problem concerns two Israeli military checkpoints blocking access to two neighbouring villages that the Palestinians want removed.
The dispute risks considerably delaying the transfer of control of the town, which Israeli Defence Minister Shaul Mofaz had said was to have begun on Monday.
"It is very important for us to see how the Palestinians fulfil their commitments on everything in taking responsibility in West Bank towns," he said, without specifying how long the transfer would take.
It is very important for us to see how the Palestinians fulfil their commitments ... in taking responsibility in West Bank towns ... that means dealing with the wanted Palestinians, their ability to keep order, dismantle terrorist infrastructure and prevent attacks"
Israeli defence minister
"In the first instance that means dealing with the wanted Palestinians, their ability to keep order, dismantle terrorist infrastructure and prevent attacks in the sectors where they have taken responsibility."
Israeli troops are not deployed in Tulkarim itself, and only wage specific operations within the city, such as missions to find those behind a February bombing in Tel Aviv, carried out by an Islamic Jihad member from Tulkarim.
Last Wednesday, Israel handed over limited security control to the PA in Jericho as part of a full handover that is to take four weeks to complete.
Ceding security in Tulkarim and Jericho, as well as Ram Allah, Bethlehem and Qalqilya, was a key issue agreed to at a landmark Israeli-Palestinian peace summit in Egypt early last month.
The process was deadlocked for weeks following the Tel Aviv bombing.
On Sunday evening a crude rocket was fired from the northern Gaza Strip into Israeli territory and caused no damage, Israeli military sources said.
Rocket fire from the Gaza Strip has practically stopped in the two months since Israeli Prime Minister Ariel Sharon and Palestinian leader Mahmud Abbas agreed to an informal truce.
Israeli soldiers partially withdrew
from Jericho last week
Most Palestinians groups decided at a meeting in Cairo last week to extend the informal truce to the end of the year, although one Gaza-based group said it would not honour the agreement.
Meanwhile, despite continuing international pressure against construction of new Israeli settlements in the West Bank, Israeli defence chief Mofaz has given the approval for the construction of more than 3500 new homes in Maale Adumim, east of Jerusalem.
"The defence minister two months ago signed off on development plans for Maale Adumim which were approved five years ago," said a ministry spokesman.
A residential suburb of 28,000 people, Maale Adumim is one of the most important Jewish settlements in the West Bank.