The Israeli navy denied reports that it issued any ultimatum to the ship. Organisers on board said the navy warned it would take over the ship if it did not change course.
Ahmed Aboul Gheit, the Egyptian foreign minister, said earlier on Tuesday that Egyptian authorities would unload the aid and distribute it into Gaza if the ship docks at El-Arish.
The ship set sail from Greece on Saturday. The Israeli government has warned that allowing the ship to breach the Gaza blockade would have "very serious consequences" for Israeli security.
"Israel will not let the boat reach Gaza," Yossi Peled, a minister in the Israeli cabinet, said on Sunday.
PJ Crowley, the US state department spokesman, urged the Al-Amal to "act responsibly".
"We have urged the Libyan government to avoid any unnecessary confrontation," he said. "We... have urged all those wishing to deliver goods to do so through established channels, so their cargo can be inspected by the government of Israel and transferred by land crossings into Gaza."
An attempt by a flotilla of aid vessels to breach the blockade in May led to the deaths of nine pro-Palestinian activists after Israeli commandos boarded the lead ship.
Following an international outcry over the raid, Israel recently eased restrictions on the Gaza Strip, allowing some previously-banned items into the territory. But construction materials remain heavily restricted, Gazans have very limited freedom of movement, and Israel still enforces a naval blockade of the territory.