Armed supporters of Fatah and Hamas have waged gun battles in the Gaza Strip in recent days.
The fighting - triggered by the announcement of early elections by Palestinian leader Mahmoud Abbas - has continued despite a ceasefire agreed on Sunday.
A raid on a Palestinian security training camp killed one person on Sunday. Hamas, which opposes the proposed poll, was blamed but denies carrying out the attack.
On Monday British Prime Minister held talks in the West Bank with Palestinian Authority President Mahmoud Abbas to reaffirm his support.
Mr Blair also met Israeli Prime Minister Ehud Olmert, who also said the moderate Palestinian leader should be supported.
All schools in the Gaza Strip were closed on Tuesday, after children got caught up in fighting. Deputy Education Minister Muhammed Abu Shaqir described the situation as anarchy.
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