Israeli public radio said on Thursday that further movements into northern Gaza, where troops have rolled across the border in an effort to free the conscript, have been delayed.
An Israeli army spokeswoman refused to confirm operations had been halted but said "our forces have not entered the northern Gaza Strip and will be ready to do so when they receive the order".
The Israeli Haaretz newspaper said on its website that the delay was decided after talks between Ehud Olmert, the prime minister, Amir Peretz, the defence minister, and security officials.
The move was prompted by an appeal from Egypt to let diplomacy run its course, Haaretz said.
The paper pointed out that the army has not stopped military operations in Gaza, but has halted "further offensive measures at this stage".
Israel was urged to spare civilians
from the military conflict
The decision to cancel Thursday night's planned operation followed international appeals for restraint, particularly from the G8 group of industrialised nations, including the US and Russia, as well as Kofi Annan, the UN secretary-general.
Earlier, Peretz had given the green light for further incursions into Gaza but also ordered the monitoring of the Palestinian humanitarian situation after international appeals to spare civilians from the military conflict.
"We are in one of the most significant moments with respect to deciding the rules of the game between us and terrorist elements in the Palestinian Authority," Peretz was quoted as saying.
The reports gave no details on what sort of operations could be expected.
Also on Thursday, the electricity distribution networks in the northern and southern Gaza Strip were hit by explosions.
Palestinian witnesses and officials said two power transformers in northern Gaza were struck, plunging parts of the area into darkness.
Israeli military officials said they were not aware of electricity infrastructure being targeted.
Airstrikes damaged Gaza's main power transformers elsewhere in the territory on Wednesday.