The war in the Middle East spread to Lebanon when Hezbollah launched a rocket attack at Israel early Monday, to "avenge" the killing of Iranian supreme leader Ali Khamenei in the US-Israeli attack on Tehran.

That prompted a swift retaliation from Israel, which has continued to bomb Lebanon since. It has also ordered the evacuation of hundreds of square kilometres (miles) of southern Lebanon and sent ground forces across the border.

"Large-scale cross-border movements" have been taking place in recent days, said Mathieu Luciano, the Lebanon mission chief for the International Organization for Migration.

"Nearly 50,000 Syrians have crossed from Lebanon into Syria over the past week, not including those who may have crossed yesterday following the evacuation orders," he added in a statement.

IOM spokesman Mohammedali Abunajela said the escalating violence in the Middle East was raising serious concerns about further civilian suffering and displacement in a region "already facing immense challenges."

"Alarming signs of population movement are already emerging, particularly in Lebanon and across the border into Syria," he told journalists in Geneva.

Ayaki Ito, emergencies chief and cross-regional refugee coordinator for the UN's refugee agency (UNHCR), said the conflict in Lebanon had "pushed many Syrian refugees residing in Lebanon to go back to Syria".

"Some of them had already planned to return even before the conflict -- but others, they are fleeing to go back home," he told journalists in Geneva.

The UNHCR official said more than 3,000 Lebanese had crossed over into Syria to flee the conflict.