In a televised address, Hayya confirmed the killing of the group's senior commander Raed Saed in an Israeli strike a day earlier.
It was the highest-profile assassination of a senior Hamas figure since a US-backed Gaza Strip ceasefire deal came into effect in October.
Thousands of Hamas supporters rallied in central Gaza City at a funeral for Saed and three associates killed alongside him on Saturday.
The mourners chanted "Martyrs are dear to God" and carried the bodies in coffins draped in green Hamas flags, in one of the group's biggest displays of its presence since a US-backed ceasefire deal came into effect in the Gaza Strip in October.
"The continued Israeli violations to the ceasefire agreement ... and latest assassinations that targeted Saed and others threaten the viability of the agreement," Hayya, who lives in exile, said in an address.
"We call on mediators, and especially the main guarantor, the US administration and President Donald Trump to work on obliging Israel to respect the ceasefire and commit to it."
Hamas sources have described Saed as the second-in-command of the group's armed wing, after Izz eldeen Al-Hadad.
Israel says Saed was one of the key architects of the October 7, 2023 attack on Israel that triggered the war.
Hayya also spoke about the proposed United Nations-authorised International Stabilisation Force (ISF).
"The role of the international forces should be limited to maintaining the ceasefire and separating the two sides along Gaza borders...without any role inside the strip or intervention in its domestic affairs," he said.
Deployment of the force is a key part of the next phase of Trump's peace plan.
Under the first phase, a fragile ceasefire in the two-year-old war began on October 10 with Hamas releasing hostages and Israel freeing detained Palestinians.
The US Central Command will host a conference in Doha on December 16 with partner countries to plan the International Stabilisation Force for the enclave, US officials told Reuters.
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