The meeting comes as a Palestinian was shot dead by Israeli forces in clashes along the border between Gaza and Israel.
A senior Hamas source, speaking on condition of anonymity, said the leadership would meet in the evening in Gaza City to discuss a number of issues, including a possible agreement.
It will be the full first meeting of the movement's political bureau since talks held in Cairo in 2017, officials said.
Among those attending will be Hamas's deputy leader Saleh al-Aruri, who crossed the border from Egypt on Thursday with eight other Hamas leaders based outside Gaza.
Aruri, who lives in Lebanon and has never before visited Gaza as he is wanted by Israel, was given Egyptian and United Nations assurances over his safety, the Hamas source said.
Israeli Prime Minister Benjamin Netanyahu on Thursday delayed a planned visit to Colombia amid speculation that a truce agreement could be reached within days.
Such a deal would involve a long-term cessation of hostilities between Israel and Hamas in exchange for a significant easing of the Jewish state's crippling economic blockade of Gaza, according to Hamas and UN officials.
An agreement could allow international donors to fund a series of programmes including electricity and water network upgrades in Gaza.
It could also cover a prisoner exchange with Hamas, which holds the bodies of two soldiers killed in a 2014 war, Israeli media say.
Palestinian shot dead
On Friday Ezzat al-Rishaq, a member of the Hamas political office, told protesters along the border they were "committed to calm".
"We do not want war and we are determined to spare our people in Gaza a new war," he said.
A Palestinian on the Gaza border was shot dead by Israeli soldiers on Friday, in the latest round of deadly clashes on the frontier.
Ahmed Yaghi, 25, was killed by a sniper east of Gaza City according to the enclave's health ministry.
More than 50 people were wounded, the ministry's spokesman Ashraf al-Qudra said.
At least 158 Palestinians have been killed in border demonstrations which began at the end of March, while one Israeli soldier has been shot dead.
According to the Israeli army, some 8,000 Gazans gathered at different spots along the frontier Friday, attempting to sabotage the Israeli border fence.
"A number of suspects infiltrated into Israel from the southern Gaza Strip, hurled firebombs and an explosive device in the border fence area and then returned into the Gaza Strip," an army statement said.
It said a tank struck a Hamas post in response.
Israeli forces also launched tear gas at protesters, who had set tires alight along the border.
Palestinians have also flown balloons and kites attached to incendiary devices across the border, starting hundreds of fires inside Israel in recent months.
With borders to both Egypt and Israel largely sealed in recent years, Gaza suffers from desperately high rates of poverty and unemployment.
Israel insists its blockade is necessary to isolate Hamas, with which it has fought three wars since 2008.
Critics say it amounts to collective punishment of the coastal territory's two million residents.
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