"Last night, IDF (army) troops managed to establish operational control of the Gazan side of (Rafah) crossing," the main entry point for aid deliveries to the besieged territory, the military said in a briefing.

"Right now at the moment what's happening, we have operational control over the Gazan side of Rafah crossing, and we have special forces scanning the area to find additional terror infrastructure or terrorists," the military said.

"The operation is not over yet. It's ongoing."

The military said ground troops were carrying out an operation in eastern Rafah.

"Overnight, IDF ground troops began a precise counterterrorism operation based on IDF and ISA (the Israeli Security Agency, Shin Bet) intelligence to eliminate Hamas terrorists and dismantle Hamas terrorist infrastructure within specific areas of eastern Rafah," the statement said.

In the briefing it said troops were engaged in a "very targeted operation and a very limited scope against very specific targets" in eastern Rafah.

On Monday, Israel ordered residents of eastern Rafah to evacuate and move to a "humanitarian zone" northwest of the city, a day after rocket fire by militants killed four soldiers and wounded several more at the Kerem Shalom crossing between Israel and the Palestinian territory.

The military said that since the start of its operation in eastern Rafah, it had killed 20 militants.

It released video footage showing a tank rolling through the Palestinian side of the Rafah crossing.

An Israeli flag is seen in the area, while drone footage showed several tanks.

"A vast amount of the organisation and the people in the area within (which) we gave the evacuation notice yesterday (Monday) moved to a safer zone," the military said.