About 250 people were arrested for trying to enter Gaza.
For at least the next six months, Israel will continue to check everyone entering or leaving southern Gaza.
Scores have been arrested by the police during protests throughout the country and amid attempts to enter Gaza illegally.
The current closing, which is open-ended, also bars foreigners from entering or leaving Gaza.
That official and the Israeli defense minister have said the government has made no decision about whether to enter Gaza.
The army confirmed only that its troops had entered central Gaza.
There are outstanding requests for over 200 people to enter Gaza and this number is growing "by the day".
One result is that anyone wishing to enter or leave Gaza must pass through an Israeli checkpoint.
On the evening of 3 January, Israeli ground troops entered Gaza.
Most of them have entered Gaza illegally, despite the army's effort to enforce a closed military zone.