Iraq has taken a key role as a mediator between Iran and Saudi Arabia since 2021, after Riyadh broke off diplomatic relations in 2016, but efforts have been deadlocked for several months.
Amir-Abdollahian, speaking to reporters in Baghdad alongside his Iraqi counterpart Fuad Hussein, hailed the efforts "to strengthen talks and cooperation between Saudi Arabia and Iran".
Since April 2021, Iraq has hosted a series of meetings between the two sides, but no talks have been publicly announced since April 2022.
"As part of the strengthening of cooperation with... the countries of the region, we welcome a resumption of relations between Iran and Saudi Arabia," he said.
Iran and Saudi Arabia have backed opposing sides in various conflicts in the region, including in Yemen.
Amir-Abdollahian also spoke to similar mediation efforts carried out between Iran and Egypt.
He also mentioned slow progress in talks in Vienna with world powers aimed at reviving the 2015 Iran nuclear accord, which promised Tehran sanctions relief in exchange for cutting back its nuclear activities.
The United States unilaterally withdrew from the deal in 2018 and reimposed sanctions, prompting Iran to begin walking back on its commitments under the accord.
Negotiations to return to the deal started in 2021 but stalled last year.
Iran is ready "to take steps to conclude the negotiations... on the basis of previous discussions and respecting the red lines" defined by Tehran, Amir-Abdollahian said.
"But if the American side chooses another path... all options are on the table", he added, without elaborating.
His Iraqi counterpart pleaded for a resumption of talks.
"It is important for Iraq that the Iranian and American parties reach an agreement", Hussein said.
The two ministers also discussed security on their border, after Iran last year bombed Iranian Kurdish opposition groups sheltering in northern Iraq.
Tehran accuses Iraq-based Kurdish groups of carrying out attacks in Iran, and of encouraging the months-long protests that erupted after the September 16 death in custody of 22-year-old Kurdish-Iranian woman Mahsa Amini, following her arrest for an alleged breach of dress rules.
Iraq later redeployed border guards to limit tensions.
"The Iraqi government has taken a series of measures to protect the frontier, and we agree that certain groups should not be allowed to cross this border," Hussein said.