Jerusalem has not yet released information on the results of Gilad's meeting in Egypt.
Taha reiterated the group's calls for a lifting of the blockade imposed on the impoverished and devastated Gaza Strip by Israel and Egypt as a condition for the truce. "[Hamas] called for a complete lifting of the blockade and an opening of all the crossings," Taha said.
Hamas proposed to Egyptian mediators that European and Turkish monitors be present at the border crossings, but rejected the presence of Israeli monitors, saying Israeli monitoring was "a large part of the problem," according to Taha.
Asked if Palestinian President Mahmoud Abbas's forces would be present at the crossings, Taha said: "Hamas is the existing government in Gaza."
Hamas wrested control of the Gaza Strip from Abbas's Fatah faction in fighting in 2007. Egypt has ruled out opening the Rafah crossing in the absence of the Palestinian Authority and European Union observers.
Commenting on the talks, Hamas's representative in Lebanon, Osama Hamdan, told Al Jazeera satellite television on Sunday that Hamas was unwilling to alter its positions to Israel's benefit.
"The Israelis must understand that they will not achieve through politics what they failed to do militarily," Hamdan said.
Israel launched an offensive in the Gaza Strip in late December with the declared aim of ending Hamas rocket attacks on its southern communities. About 1,300 Palestinians, at least 700 of them civilians, were killed during the 22-day offensive, while Israel put its death toll at 10 soldiers and three civilians.
Hamas: No reconciliation with Fatah until it ends Israel peace talks
Hamas official Hamdan also said Sunday that Fatah movement must end peace negotiations with Israel before any reconciliation talks can take place.
The remarks were bound to complicate Arab efforts to reconcile Hamas, which controls Gaza, and the Fatah-dominated Palestinian Authority in the West Bank.
Speaking at a rally in Beirut Sunday, Hamdan - a close ally of Hamas political leader Khaled Meshal - said that the group welcomed Palestinian dialogue, but any reconciliation should be based on a resistance program to liberate territory and regain rights.
He also demanded that the PA end security coordination with Israel, and maintained that the Israeli-Palestinian peace process had ended.
"Those who committed mistakes must correct their mistakes through a clear and frank declaration to stop security coordination with the [Israeli] occupation, release [Hamas] prisoners and later end negotiations [with Israel] because the peace process is irreversibly over," said Hamdan.
"It's time for us to talk about a reconciliation based on a resistance program to liberate the [occupied] territory and regain rights," he added.
Hamas: No mediated truce unless Gaza borders opened
Earlier Sunday, Hamas spokesman Fawzi Barhoum said that the Islamist militant group would not accept any mediated truce agreement with Israel in Gaza unless Israel reopened the Palestinian territory's border crossings.
Barhoum made the comments ahead of talks with Egyptian officials on means to reopen the Gaza border, largely closed since the group violently took over Gaza in June 2007.
"We are not going to accept less than opening the borders ... and lifting the sanctions," said the spokesman, adding that discussions would address a detailed cease-fire agreement.
The issue of the crossings is key to preserving the cease-fire declared after Israel's 3-week offensive against Hamas in Gaza. Israel, the United States and Egypt are trying to work out security arrangements to ensure Hamas does not smuggle weapons into the strip before any opening.
Another Hamas spokesman, Ayman Taha, told London-based Asharq Al-Awsat newspaper Saturday that his group wants European Union and Turkish troops to patrol Gaza's border crossings with Israel.
"We reject an open-ended cease-fire, but temporary calm with guarantees can be discussed," he also said, without specifying how long.
A low-level delegation from Hamas' rival, Palestinian President Mahmoud Abbas' West Bank-based government, is also in Cairo for talks, but is not expected to meet with the Hamas envoys.
Asharq Al-Awsat also reported Saturday that Hamas had suggested representatives of the Palestinian Authority be stationed at the Rafah crossing, but that they be residents of Gaza, not the West Bank.
Israel has been allowing some supply convoys into Gaza, though its borders remain largely closed. The Israel Defense Forces says more than 125 trucks a day - on some days nearly 200 - have entered Gaza since fighting ended on January 17th, but aid workers say the numbers are not enough.