Hamas called on mediators to prevent Israel breaching the ceasefire in Gaza during talks with Egyptian officials on Sunday, after 22 Palestinians were killed in Israeli bombing the previous day.
Israel also killed four more people in the Gaza Strip on Monday.
A delegation led by the group's political bureau chief Khalil al-Hayya met with Egyptian intelligence chief Hassan Rashad in Cairo to discuss the ceasefire and moving to its second phase.
Egypt has worked with Qatar and the US to mediate an end to Israel's two-year genocidal assault on the Palestinian territory.
In a statement following the meeting, Hamas said it remained committed to upholding the first phase of the truce but called on the mediators to implement a "clear and defined mechanism" to monitor and prevent continued breaches of the ceasefire by Israeli forces.
Israel has violated the ceasefire almost 500 times since it came into force on 10 October, according to the Gaza government media office.
As of yesterday, the Israeli military had killed 339 Palestinians and wounded 871 others in the six weeks since the truce came into effect.
The Cairo meeting came on the heels of one of the deadliest days in Gaza since the ceasefire came into effect.
22 Palestinians were killed and dozens more wounded in another round of bombing that Israel claimed was a response to a Hamas gunman opening fire on its troops.
The Palestinian group denied the accusation and said Israel was looking for "an excuse to kill".
Second phase
Hamas said it also discussed with Egyptian officials moving to the second phase of the ceasefire agreement and the fate of almost 200 Hamas fighters thought to be trapped in tunnels beneath Israel-occupied Rafah.
Last Friday, Israel killed six of the fighters who emerged from the tunnels, while capturing another five.
Under the second phase of the Gaza ceasefire deal, a technocratic Palestinian administration is supposed to be established to govern Gaza and manage the reconstruction process. It will be overseen by an international "Board of Peace" chaired by US President Donald Trump.
It also calls for the deployment of a multinational peacekeeping force to provide security and train Palestinian police, but several Arab and Muslim countries originally slated to provide troops to the force have now expressed reluctance.
Israel and the US have demanded that Hamas surrender its weapons though the Palestinian group has refused until Israel agrees to end the occupation and allow the creation of a Palestinian state.
The Trump plan was endorsed by the UN Security Council earlier this month.
Four Palestinians killed
Israeli forces continued their attacks in Gaza on Monday morning in breach of the ceasefire, killing four Palestinians.
Al Jazeera reported that drones opened fire in Gaza City and Khan Younis on people who had crossed the so-called "yellow-line" that demarcates Israel-occupied Gaza.
Medics said that four people had been killed and at least two others wounded.
Israeli forces have frequently opened fire on people who had crossed the largely invisible boundary that separates Hamas-run and Israel-occupied Gaza.
Israel continues to occupy more than half of the territory under the terms of the ceasefire.