Over a million people have been displaced from the Gazan city of Rafah amid Israel's ongoing military operations there, according to the United Nations agency for Palestinian refugees (UNRWA).

The small city on the southern edge of the Gaza Strip had been sheltering around 1 million Palestinians who fled Israeli assaults on other parts of the enclave, the aid group said Monday.

Since early May, Israel's military has been carrying out what it says is a limited operation in Rafah to root out the Palestinian resistance group Hamas and dismantle their infrastructure.

The Israeli military has told civilians to go to an "expanded humanitarian zone" some 20 kilometers (12 miles) away.

Many Palestinians have complained they are vulnerable to Israeli attacks wherever they go, and have been moving up and down the Gaza Strip in the past few months.

UNRWA said thousands of families now shelter in damaged and destroyed facilities in the city of Khan Younis, where the agency is providing essential services despite "increasing challenges."

"Conditions are unspeakable," the agency added.