Oil prices were uncertain during Asian trading hours on Tuesday as signs of a breakdown in the U.S.-Iran nuclear deal eased some concerns about oversupply, but the prospect of ceasefire talks between Russia and Ukraine weighed on sentiment.

Brent crude futures expiring in June remained at $65.55 a barrel as of 22:03 ET, while West Texas Intermediate (WTI) futures edged up 0.1% to $62.20 a barrel.

Iran reiterated on Monday that its uranium enrichment program is "absolutely not negotiable," a stance that continues to be a major obstacle in nuclear talks with the United States.

The United States has demanded that Iran halt all uranium enrichment activities, citing concerns about potential nuclear weaponization. Special envoy Steve Witkoff reiterated that any new deal must ban Iran from enriching uranium, a position Iran steadfastly rejects.

The standoff has caused market volatility, with oil prices fluctuating on concerns that the talks could collapse.

If the deal is successfully reached, it could lead to the easing of sanctions and an increase in Iranian oil exports, affecting global energy markets.

Russia and Ukraine will "immediately" begin ceasefire negotiations to end the ongoing war, US President Donald Trump announced on Monday after a phone call with Russian President Vladimir Putin.

"I thought the call went very well. Russia and Ukraine will immediately begin negotiations to reach a ceasefire and, more importantly, an end to the war," Trump said.

Putin described the efforts as "on the right track" and expressed his readiness to work with Ukraine on a potential peace deal.

However, the Kremlin has yet to commit to an unconditional ceasefire. Trump has proposed holding future peace talks at the Vatican and said the United States could reduce its involvement if the negotiations stall.

"The scheduled call between President Trump and President Putin did not appear to result in any significant breakthrough," ING analysts said in a note.

Investors are watching the situation closely as the resolution of the conflict could affect energy markets and geopolitical stability.