Egypt has occasionally opened the Rafah crossing - the only Gaza crossing that bypasses Israel - to allow aid in and students and medical cases out.
In a surprise visit to the crossing, Ismail Haniya, the Hamas leader, said he hoped to see its "complete" re-opening.
"We are prepared and ready [to operate the crossing] according to arrangements undertaken with our Egyptian brothers, the Europeans, the presidential guard [of Mahmoud Abbas, the Palestinian president] and the [Hamas-run] government."
Egypt has consistently rejected pressure to open its border with the Gaza Strip permanently, insisting it can only do so when the Abbas' authority has been restored.
An international agreement signed by Israel and Abbas' Palestinian Authority in 2005 provided for EU monitoring of all traffic across the border and the installation of Israeli security cameras.
But Hamas has rejected any Israeli presence at the crossing.