Any such move seems remote for the time being, however.
Gaza's Egyptian border crossing at Rafah was blasted open last week by Hamas Islamists, allowing hundreds of thousands of Palestinians to pour across to stock up on supplies in defiance of an Israeli-led blockade of the Hamas-controlled territory.
European border monitors had been stationed at Rafah until June, when Hamas routed secular Fatah forces loyal to Palestinian President Mahmoud Abbas. Abbas has since wielded little authority beyond the Israeli-occupied West Bank.
"The EU is ready to consider resuming its monitoring mission in Rafah under the provisions of the relevant international agreements related to the Access and Movement concluded in November 2005," EU foreign ministers said in a statement.
Such a move was conditional on prior agreement between the Palestinian Authority, Egypt and Israel on the movement of persons, the ministers said in a statement in which they expressed "grave concern at the humanitarian situation in Gaza".
The EU urged Israel to fulfill its obligations to the Hamas-led territory and called for the continuous provision of essential goods and services including fuel and power supplies.
Arab foreign ministers meeting in emergency session in Cairo on Sunday welcomed a suggestion by Palestinian President Mahmoud Abbas that the Palestinian Authority would take control of the border and run the crossing.