Israel's statement on the meeting, in which it said the ministers had discussed possible cooperation, prompted small protests in Libya, which does not recognize Israel.
Libya's Foreign Ministry said Mangoush had rejected a meeting with representatives of Israel and that what had occurred was "an unprepared, casual encounter during a meeting at Italy's Foreign Affairs Ministry."
The Libyan ministry's statement said the interaction did not include "any discussions, agreements or consultations" and added the ministry "renews its complete and absolute rejection of normalization" with Israel.
Since 2020 Israel has moved to normalize ties with the United Arab Emirates, Bahrain, Morocco and Sudan through the so-called "Abraham accords" brokered by the United States.
"I spoke with the foreign minister about the great potential for the two countries from their relations," Israel's Cohen said in a statement.
Israel's foreign ministry said the meeting was facilitated by Italian Foreign Minister Antonio Tajani, adding that they had discussed possible cooperation and Israeli aid in humanitarian issues, agriculture and water management.
Cohen said he had spoken to Mangoush about the importance of preserving Jewish heritage in Libya.
Libyan foreign policy is complicated by its years of conflict and its bitter internal divisions over control of government and the legitimacy of any moves made by the Tripoli administration.
The Government of National Unity was installed in early 2021 through a U.N.-backed peace process, but its legitimacy has been challenged since early 2022 by the eastern-based parliament after a failed attempt to hold an election.
Previous foreign policy moves by the GNU — including agreements it has reached with Turkey — have been rejected by the parliament and subjected to legal challenges.
The Presidency Council, which functions as head of state, issued a statement on Sunday asking GNU Prime Minister Abdulhamid al-Dbeibah for clarification on what had taken place.
The High State Council, which holds an advisory role in Libyan politics, voiced its "surprise" at the reports of the meeting and said those responsible "should be held accountable."