Brent crude futures climbed $3 to reach $104.32 a barrel, while West Texas Intermediate followed with a similar gain.
The rejection sparked fresh concerns over global energy supplies as the critical Strait of Hormuz remains largely closed.
Market analysts believe both nations remain far apart on a final agreement despite active behind-the-scenes diplomatic channels.
Traders originally expected a swift resolution last week, but the current deadlock keeps the international market exceptionally tight.
President Trump travels to Beijing on Wednesday to seek Chinese assistance in pressuring Iran toward a viable deal.
Saudi Aramco reports that the world lost roughly 1 billion barrels of oil over the past two months.
Shipping data shows some tankers navigating the region with trackers switched off to ensure safe transit of crude.
Experts predict prices will remain high until maritime trade routes return to a state of full normalization.
