Mr Blair, who was Prime Minister at the time, supported President George W Bush's push to halt aid to and cut ties with the newly elected Hamas-led Palestinian authority unless it agreed to recognise Israel and renounce violence.
In an online posting later, Netanyahu warned that the deal would make "peace much harder to achieve".
"Israel should end its siege on Palestinian lands and avoid any movement that would harm the reconciliation process", he said.
Mr Blair was appointed Special Envoy of the Middle East Quartet, which comprises of the US, EU, UN and Russian Federation, the day he resigned as Prime Minister. It also called for the immediate release of Israeli civilians Avra Mengistu and Hisham a-Said, who are being held by Hamas, and the remains of fallen Israeli soldiers Oron Shaul and Hadar Goldin.
Education Minister Naftali Bennett, leader of the nationalist Jewish Home party, blasted the deal.
After a decade of hostility and recrimination, the two main Palestinian factions came together in Cairo on Thursday to sign a reconciliation deal that holds out the tantalizing prospect of a united Palestinian front.
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In 2007, when the two groups could not agree on sharing power, Hamas drove Fatah leaders out of Gaza and wrested control of the seaside territory, leaving Palestinian Authority President Mahmoud Abbas in control only of parts of the West Bank.
Abbas was adamant before the talks began that no unity government would be formed without Hamas completely disarming.
The Palestinians said they were establishing committees to iron out details about security, elections, salaries and other administrative details in this latest try at unity government, but there was little or no mention of Israel at their press conference in Cairo on Thursday.
"There is nothing Israel wants more than peace with all our neighbors".
If this deal succeeds, the Palestinian territories of the West Bank and Gaza will be reunited under one leadership for the first time since the Islamist militant group Hamas wrested control of the territory 10 years ago.
All previous Fatah-Hamas attempts to reconcile have quickly broken down.