Abdelatty's discussions with Mladenov are part of Egypt's ongoing consultations on developments in Gaza and preparations for the next stage of the peace plan, the Egyptian Foreign Ministry said.
The two officials followed up on the roadmap for completing commitments under the Gaza peace plan.
Abdelatty stressed the importance of all parties fulfilling their agreed commitments, including ensuring full, safe, and sustainable access for humanitarian aid and completing the Israeli withdrawal from Gaza, paving the way for the second phase of the plan and supporting early recovery and reconstruction efforts.
The talks also addressed arrangements for the next phase.
Abdelatty stressed the importance of enabling the National Committee for the Administration of Gaza to begin carrying out its temporary duties from inside the territory, while moving ahead with arrangements to deploy the International Stabilization Force to monitor the ceasefire and support security and stability during the transitional period.
He also stressed that these arrangements must preserve the territorial unity of the Palestinian territories and ultimately enable the Palestinian National Authority to assume its full responsibilities in Gaza and the West Bank.
The talks came hours after Israeli Prime Minister Benjamin Netanyahu rejected Trump's 15-point proposal, saying on Sunday that Israel would not withdraw its forces from Gaza until Hamas is "genuinely" disarmed.
"Israel rejects the 15-point document," Netanyahu said at a cabinet meeting on Sunday, according to Reuters.
Netanyahu said the Israeli military would not withdraw until Hamas had been disarmed, including of its heavy and other weapons. Israel has therefore rejected a central element in the sequencing of the US-backed roadmap, which envisages Hamas disarmament alongside an Israeli withdrawal and the deployment of an international stabilization force.
Trump's Board of Peace said last month that it had reached an agreement with Hamas on the "complete disarmament" of Hamas and other armed groups in Gaza. Hamas, however, has conditioned the handover of its weapons on an end to Israeli attacks and the withdrawal of Israeli forces from the territory.
The dispute over sequencing has emerged as a major obstacle to moving into the next phase of the Gaza plan.
Hamas has agreed to the roadmap under Egyptian mediation and indicated that its weapons could be placed under a US-supervised Palestinian administration. However, it has rejected unconditional disarmament while Israeli forces remain in Gaza.
A further obstacle concerns the National Committee for the Administration of Gaza, which is intended to assume temporary responsibility for the territory during the transitional period.
The committee has yet to begin operating from inside Gaza, with Israel continuing to prevent its members from entering the enclave, according to Palestinian and regional officials.
Established as part of arrangements for Gaza's post-war administration, the committee is intended to provide temporary technocratic governance and oversee the restoration of basic services.
Egypt has repeatedly stressed the importance of enabling the committee to operate from inside Gaza as part of the process toward Palestinian administration of the territory.
Against the backdrop of the latest disagreement between Washington and the Israeli government, Abdelatty stressed the need for all parties to honour their commitments and refrain from measures that could obstruct implementation or undermine progress already achieved.
He also underscored the importance of continuing efforts to consolidate stability in Gaza and create the necessary conditions for moving to the next stage of the peace plan.
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