The Islamist militant group has controlled the coastal strip for a year now and says it will not relent to international pressure.
On his second trip to Israel, President Bush will address the issue of settlement building and try to push for progress on a two-state solution to the Israeli-Palestinian conflict.
The former president said Monday that the Islamist militants are prepared to accept the right of Israel to 'live as a neighbor next door in peace.'
The former president arrived in Israel Sunday as Palestinians in Gaza continued to cope with an Israeli-imposed fuel blockade.
The men were detained after militants from Gaza breached the border in January. Egypt continues to hold one of them.
Israeli officials see opportunity to turn Gaza over to Egypt to provide services.
In an interview, key Hamas strategist Mahmoud Zahar discusses how his movement has been preparing for a potentially imminent Israeli assault on Gaza.
Supporters see hope in printing a tale in which enemies make peace.