The demands go further than a return to the truce brokered in Cairo in 2012, to put an end to eight days of fighting in the Gaza Strip. That truce included a pledge to open a border crossing, intending to ease the blockade of the coastal enclave.
Yesterday, Meshaal said an easing of the restrictions was no longer acceptable and Hamas would stop at nothing short of a "full and permanent" lifting of the blockade that, as well as regulating the traffic of people and goods at the border, forbids trade from Gaza's port.
Since General Abdelfattah al-Sisi, who considers Hamas a terrorist organisation, became President of Egypt earlier this year, Gaza's Rafah border crossing with its neighbour has also remained mostly closed.
Sisi also blocked tunnels between Egypt and the Gaza Strip, which had become a vital supply line of goods for civilians which are banned under the blockade and weapons for the enclave's armed groups.
Meshaal refused to expand on the details of how the siege would be lifted, saying that it was being discussed by mediators privately.
Meshaal remained defiant in Hamas' decision to continue firing rockets into Israel. When asked whether firing the rockets, which are largely ineffective in the face of Israel's protective Iron Dome shield, was worthwhile in the face of so many Palestinian deaths, Meshaal said: "If the rockets are not effective, why is the international community pushing for a ceasefire?"
He said the calculation was "not about the impact of each rocket" but the political effect that they have in Israel, and that they were a symbol of the Palestinians' will to resist "occupation".
The Hamas leader said the Palestinian issue could no longer just "be placed on the table for discussion" and that, this time, it had to be resolved.
He insinuated that, with the latest round of peace talks, led by John Kerry, the United States Secretary of State, having failed, a return to violent "resistance" had become necessary.
Tensions between Israelis and Palestinians reached boiling point over the deaths of the three students. Israel named Marwan Qawasmeh and Amar Abu Aisha, two members of Hamas from the West Bank city of Hebron, as the perpetrators of the killings.
Meshaal said Israel had no evidence on which to base the accusation, other than that the two operatives had gone underground at about the same time that the students were captured and killed.
He said his organisation had no information about how the incident came about, and could neither confirm nor deny responsibility.
