In a statement on Wednesday, the movement said Haniyeh held "communications with the mediators in Qatar and Egypt regarding the ideas being discussed with them to reach an agreement that would put an end to the brutal aggression faced by our steadfast people in the Gaza Strip."
Haniyeh also spoke "with officials in Turkey regarding the recent developments," the readout said, adding that the movement has "engaged positively."
Israel has killed nearly 38,000 Palestinians, mostly women and children, since Oct. 7, 2023. The Israeli military onslaught has left the coastal enclave in ruins.
Mediators delivered a response from Hamas to a proposal that would include the release of captives held in Gaza and a ceasefire in the territory.
Israel is evaluating the remarks and will convey its reply to the mediators, said a statement released by the office of the regime’s prime minister Benjamin Netanyahu.
Egypt and Qatar are among the countries that have been trying for months to secure a truce.
A seven-day truce, mediated by Doha and Cairo in November, saw Hamas releasing 105 of the captives that had been seized during Al-Aqsa Storm for 240 Palestinian prisoners.
In early May, Hamas agreed to another truce proposal enabling the cessation of the Israeli aggression and release of the rest of the captives. The Israeli regime, however, rejected the proposal.
Hamas says another truce deal has to end the war, bring about complete withdrawal of the Israeli forces from the coastal sliver, and involve a genuine captive/prisoner exchange deal.