It comes amid reports that PM Netanyahu is pushing to expand Israel's military operations in Gaza.
Dozens are missing after a boat carrying more than 150 migrants, many believed to be Ethiopian, sank in bad weather.
The Palestine Red Crescent Society accuses Israel of a "direct" strike - Israel says it is reviewing the claim.
Hamas said it would allow Red Cross access if humanitarian aid corridors were opened into Gaza.
Far-right minister Itamar Ben-Gvir prayed at Jerusalem's al-Aqsa mosque compound, violating a decades-old arrangement.
Evyatar David's family says Hamas is starving him, as the group shows a video of him being kept in a tunnel.
Negotiations between Israel and Hamas for a ceasefire and the release of hostages stalled last week.
Some say Britain's decision is an important first step – while others worry it won't make a real difference, writes BBC's International Editor Jeremy Bowen.
The visit with the IDF follows near daily reports of deadly shootings in the vicinity of the sites.
The Palestinian student, who arrived in France in July, has had her university accreditation withdrawn.
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