The three sons - Hazem, Amir and Mohammad - were killed when the car they were driving in was bombed in Gaza's Al-Shati camp. Four of Haniyeh's grandchildren, three girls and a boy, were also killed in the attack.
The Israeli military said there was "no information on that right now."
Haniyeh, based in Qatar, has been the tough-talking face of Hamas' international diplomacy as war with Israel has raged on in Gaza, where his family home was destroyed in an Israeli airstrike back in November.
"The blood of my sons is not dearer than the blood of our people," Haniyeh, 61, who has 13 sons and daughters according to Hamas sources, told pan-Arab Al Jazeera TV.
The three sons and four grandchildren were making family visits during the first day of the Muslim Eid al-Fitr holiday in Shati, their home refugee camp in Gaza City.
Hamas said on Tuesday it was studying an Israeli ceasefire proposal in the more than six-month-old Gaza war but that it was "intransigent" and met none of the Palestinian demands.
"Our demands are clear and specific and we will not make concessions on them. The enemy will be delusional if it thinks that targeting my sons, at the climax of the negotiations and before the movement sends its response, will push Hamas to change its position," Haniyeh said.
In the seventh month of a war in which Israel's air and ground offensive has devastated Gaza, Hamas wants an end to Israeli military operations and a withdrawal from the enclave, and permission for displaced Palestinians to return home.
Haniyeh's eldest son confirmed in a Facebook post that his three brothers were killed. "Thanks to God who honoured us by the martyrdom of my brothers, Hazem, Amir and Mohammad and their children," wrote Abdel-Salam Haniyeh.
Appointed to the militant group's top job in 2017, Haniyeh has moved between Turkey and Qatar's capital Doha, avoiding Israeli-imposed travel restrictions in blockaded Gaza and enabling him to act as a negotiator in the latest ceasefire negotiations or communicate with Hamas' main ally Iran.
Israel regards the entire Hamas leadership as terrorists, accusing Haniyeh and other leaders of continuing to "pull the strings of the Hamas terror organization".
But how much Haniyeh knew about the October 07 cross-border attack on Israel by Gaza-based militants beforehand is not clear. The attack plan, drawn up by the Hamas military council in Gaza, was such a closely guarded secret that some Hamas officials abroad seemed shocked by its timing and scale.
