Ayman Taha, a Hamas official, said the proposals would be discussed further with the group's leadership in Damascus.
"We will study the matter again and it will be brought back to the Egyptians," he told MENA, the official Egyptian news agency on Sunday, without elaborating on the other provisions of the possible deal.
Amos Gilad, Israel's top negotiator on Gaza, was in Cairo last week for talks.
The 22-day Israeli offensive which began on December 27 killed some 1,300 Palestinians and left more than 5,000 others wounded.
Taha said the discussions with Omar Suleiman, the Egyptian intelligence chief, covered the nature and length of the truce, a system to monitor the border crossings and how reconstruction would be carried out.
|Thousands of Palestinian homes
have been destroyed [AFP]
"We are ready for any help in this issue [of reconstruction], but we are not willing to make it a political issue or use it for blackmail," he told the news agency.
Hamas has rejected the presence of Israeli monitors at border crossings, calling instead for monitors to come from the EU and Turky.
The counter proposal follows a Hamas pledge of $50m of its own money for the reconstruction of the Gaza Strip, saying that it alone should supervise the effort.
A national committee set up to oversee relief efforts will start giving out the money this week to Palestinians afflicted by the Israeli offensive.
On Sunday Ahmed al-Kurd, the Hamas-appointed social affairs minister who also heads the committee, said the money will be distributed to those who lost family members or their homes.
He said more than 20,000 Palestinian houses have been either completely or partially destroyed during the recent war.
The Palestinian Authority of Mahmoud Abbas, the Palestinian president, has also asked to lead the reconstruction efforts, which it said would require about $1.9bn in aid.
The Fatah group led by Abbas was forced out of power in Gaza when Hamas took control of the Gaza Strip in June 2007.
According to initial estimates Gaza suffered about $2bn in damage during the Israeli air strikes and ensuing ground offensive.
Israel and the US have opposed reconstruction funds for Gaza going to Hamas.