A small Israeli force has entered the Gaza Strip to search for tunnels and mines, military sources have said.
Israeli tanks and armoured vehicles were massing on the border
Tanks and bulldozers moved into the north of the territory, but military sources said it was not part of a threatened large-scale incursion.
The penetration into northern Gaza was the first time Israeli troops had entered the area since a soldier was abducted last week.
Israel has launched strikes against Gaza to try and speed his release.
The units sent into northern Gaza were there "to conduct pinpoint operations to find tunnels and explosive devices", military sources were quoted as saying.
A witness on the border said "around 25 Israeli tanks crossed the border in waves of eight tanks", AFP news agency said.
On Sunday, tanks massed on the Israeli border and aircraft and artillery pounded northern Gaza, as Israeli Prime Minister Ehud Olmert told his army to "do all it can" to free the captured soldier, 19-year-old Cpl Gilad Shalit.
The military wing of the governing Palestinian party, Hamas, has said it will attack targets inside Israel if Israel does not end its Gaza offensive.
Militants have used the area to launch unguided rockets into Israeli territory.
The Palestinian prime minister's office was hit in an attack
Egyptian-brokered negotiations with the three militant groups which had claimed responsibility for abducting the soldier have not had any success.
There have been no confirmed reports about Cpl Shalit's condition.
Israel has refused to discuss a prisoner exchange with the Palestinian authorities. The soldier's captors had demanded the release of nearly 500 prisoners held in Israeli jails in exchange for the corporal.
On Saturday, Israeli combat helicopters carried out a raid on the Palestinian cabinet buildings, striking the office of Prime Minister Ismail Haniya. Mr Haniya was not in the building at the time, but three security guards were hurt.
Gaza City raids
Artillery hit northern Gaza near the town of Beit Lahiya, early on Monday, injuring three people, AFP said.
Israeli military sources also said they had undertaken raids against Gaza City buildings run by the Al-Aqsa Martyrs Brigades movement, linked to Palestinian leader Mahmoud Abbas's Fatah party.
About 5,000 troops are said to be waiting on the border of the coastal Gaza Strip, which Israeli forces left in September 2005 after 38 years of occupation.
Cpl Shalit was abducted in a raid on a border post which saw two other Israeli soldiers killed.
The armed wing of the Hamas movement is one of three groups claiming to have undertaken the raid.