Israeli troops moved deeper into Gaza City Sunday and pounded Rafah from the air. Hamas rejected plans for international peacekeepers in Gaza.
The Rafah crossing is seen by Israel as a weapons supply line for Hamas and a humanitarian lifeline by Gazans.
Hamas and Israel say they are weighing an Egyptian proposal for a cease-fire as international calls to end the conflict mount.
The Islamist militants in Gaza may emerge as a symbol of defiance, much as Hezbollah did in its 2006 war with Israel.
Both sides are maneuvering for another ceasefire, and Israeli troops are not likely to invade the Gaza strip, say analysts.
Networks of tunnels underneath the Egypt-Gaza border are used to ferry everything from food to weapons into the impoverished Gaza Strip.
Hamas says that Gilad Shalit could be released in a week, but terms of a deal with Israel keep shifting.
Palestinian militants from Islamic Jihad fired rockets on Israel Tuesday in retaliation for an Israeli strike on its members in the West Bank.