An Iranian delegation last week travelled to Saudi Arabia, which cut ties in January, for discussions on the pilgrimage to the Muslim holy places in the kingdom.
Said Ohadi, head of the Iranian Hajj Organisation, said on state television late yesterday that four days of negotiations had achieved progress on security issues and travel to the kingdom.
But the lack of a functioning Saudi embassy in Tehran - both it and the kingdom's mission in Iran's second city Mashhad are closed - means there are currently no visas being issued to Iranians.
Tehran wants visas to be issued inside the Islamic republic.
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In the absence of its own representatives, Switzerland looks after the interests of the Sunni-dominated kingdom in mainly Shiite Iran.
Ohadi said the foreign ministry had offered to provide "all means necessary" to help Saudi Arabia issue visas inside Iran but did not elaborate on how that could be done in the absence of an embassy or consulate.
He said Saudi Arabia had agreed that Iranian aircraft could land for the hajj, an exception since all flights from the Islamic republic were barred after the diplomatic crisis.
"The Saudis offered good solutions on security," introducing electronic tracking bracelets for all hajj participants, Ohadi said.
Other officials in Tehran also waded into the row.
"Saudi Arabia is stonewalling on the visa issue," Culture Minister Ali Jannati said yesterday.
"We say that if the Swiss government is protecting your interests in Iran, then it should issue visas too. Issuing visas in a third country is absolutely unacceptable for us."
Saudi Arabia severed diplomatic ties with Iran on January 3 after its diplomatic missions in Tehran and Mashhad were stormed and set alight by mobs following Riyadh's execution of a prominent Shiite cleric and activist, Nimr al-Nimr.