Pro-government mobs attacked and burned Saudi embassy in Tehran in 2016.
Saudi Arabia's envoy to the United Nations said the kingdom wanted more substantive talks with Iran but that Tehran was so far biding its time and playing "games" in the discussions.
Riyadh and Tehran launched direct talks this year at a time global powers are trying to salvage a nuclear pact with Tehran and as UN-led efforts to end the Yemen war stall.
The kingdom, which cut ties with Tehran in 2016, has described the talks as cordial but exploratory, while an Iranian official in October said they had gone a "good distance".
Riyadh's UN envoy Abdallah Al-Mouallimi told Saudi newspaper Arab News in a video interview published on Monday that no major results had been achieved.
"We would like to push these discussions towards substantive issues that involve the behavior of the Iranian government in the region," Mouallimi said.
"But as long as the Iranians continue to play games with these talks, they are not going to go anywhere," he said. "The Iranians take a long-term attitude towards these talks. We are not interested in talks for the sake of talks."
Tensions between the two foes spiked in 2019 after an assault on Saudi oil plants that Riyadh blamed on Iran, a charge Tehran denies, and continue to simmer over Yemen where a Saudi-led coalition is battling the Iran-aligned Houthi group.
"It (Yemen) has proved to be intractable simply because the Houthis continue to receive a continuous supply of weapons and ammunition from their benefactors, particularly Iran," Mouallimi said, reiterating a charge that both Iran and the group reject.