The Hamas delegation arrived in Egypt on Saturday for the final round of ceasefire talks with Israel.
Mohammed Nazzal said in an interview with the Qatar-based news channel Al-Jazeera that Hamas was interested in reaching the deal as soon as possible as it wanted to put an end to the sufferings of the Palestinian people.
The delegation, led by a senior Hamas leader, Mahmoud Zahar, is expected to learn Israel's response to the Hamas group's ceasefire proposals and to give its final response on the 18-month ceasefire deal.
Hamas insists on an end to Israel's blockade of the Gaza Strip, in place since the radical Islamist group seized the territory of the Palestinian enclave in June 2007, and an opening up of crossing points for normal traffic.
Hamas left the talks in Cairo on Wednesday with no agreement in place, blaming "Israel's stubbornness in lifting the blockade of the Gaza Strip and opening the border crossings."
Egypt mediates talks between Israel and Hamas, who do not communicate directly.
Both Israel and Hamas announced a ceasefire on January 18, shortly after Israel concluded its three-week military operation in Gaza, which left more than 1,300 Palestinians dead.