Abdelatty conveyed the message in telephone calls to Iranian foreign minister Abbas Araghchi and International Atomic Energy Agency (IAEA) chief Rafael Grossi, according to a statement by the Egyptian foreign ministry on Friday.
Iran denies seeking a nuclear weapon but Western powers and Israel doubt its intentions.
Egypt's efforts aim "to support security and stability in the region by finding peaceful solutions to the Iranian nuclear file," it said, adding Abdelatty "stressed the importance of continuing the dialogue between the two sides and resuming and strengthening cooperation."
The two sides inked a deal in Cairo in September aimed at resuming full IAEA access but little progress appears to have been made.
Iran suspended cooperation with IAEA inspectors after a 12-day war in June against Israel and the United States in which they attacked Iranian nuclear sites, codified via a new law passed by parliament.
Under the post-war law, inspections proceed via Supreme National Security Council (SNSC) approval for limited IAEA access at non-stricken sites, maintaining safeguards obligations under conditional cooperation while excluding full reporting and Non-Proliferation Treaty (NPT) oversight.
Iran had warned the any concessions on inspections would be void if Western sanctions return. Since the re-imposition of UN sanctions last month, the agreement's fate with the agency remains unclear.
"We are trying to build it back, and we are inspecting in Iran," Grossi said on Wednesday. "Not at every site where we should be doing it—but we are gradually coming back."
Grossi added there was no indication of any suspicious activity at the sites attacked by Iran's foes.
The Center for Strategic and International Studies (CSIS) reported Tuesday, citing satellite imagery, that Iran has continued construction at a major underground nuclear site near Natanz.