However, energy industry watchers and experts in the region believe the Iranian leadership in Tehran is not ready for talks. They say the Islamic Republic will first seek to strengthen its hand after the Trump administration tightened sanctions on the nation's lifeblood, oil exports, and designated the Iranian Revolutionary Guard Corps a terrorist group.
That leaves room for miscalculations that could keep the oil market on edge. Tehran and Washington have already misread one another's actions, leading to a dangerous series of counter measures between the adversaries, the Wall Street Journal reported on Thursday.
Trump on Thursday met with Swiss President Ueli Maurer, whose nation has facilitated communication between the U.S. and Iran since they broke diplomatic ties in 1979. A day earlier, Secretary of State Mike Pompeo phoned Sultan Qaboos bin Said of Oman, another long-time intermediary between the U.S. and Iran.
That outreach, along with Trump's recent remarks that he wants Iran to call him, are fueling speculation that Washington is seeking a diplomatic path after a series of troubling escalations in the Middle East.
This week alone, four vessels were allegedly sabotaged in a strategic oil port off the coast of the United Arab Emirates. Iran-aligned Houthi rebels in Yemen also claimed responsibility for drone attacks on Saudi oil infrastructure, prompting retaliatory airstrikes by Saudi Arabia on Houthi positions in Yemen.
Meanwhile, Washington has expedited the deployment of warships and bombers to the Middle East and pulled diplomatic staff from Iraq in response to intelligence suggesting Iran is planning attacks on U.S. positions in the region. The posturing has raised concerns that hawks within the White House are setting the stage for military conflict.
But a day before his meeting with the Swiss president, Trump reportedly told acting Defense Secretary Patrick Shanahan that he does not want to go to war with Iran. On Friday, Trump took to Twitter to denounce the "Fake News Media" for "fraudulent and highly inaccurate coverage of Iran."
"I think they're trying to walk it back a bit," said John Kilduff, founding partner at energy hedge fund Again Capital. "I don't think Trump wants a war. I think he thinks it would hurt his reelection efforts."
Oil prices have risen about 2% this week on Middle East tensions. If the rhetoric from Washington cools, oil prices could pull back at least $2 a barrel, Kilduff said.
Risk consultancy Eurasia Group believes Trump is serious when he says he wants Iran to call him to negotiate.
"Trump is supremely confident in his negotiating abilities and believes he can strike deals that no other president can. He wants to repeat with [Iranian President] Hassan Rouhani what he did with Kim Jong Un," Eurasia Group analysts Henry Rome and Jeffrey Wright said in a research note.
Rome and Wright say the Iranian foreign minister's offer last month to negotiate a prisoner swap may have opened the door for this week's meeting with the Swiss. But following increased U.S. pressure, Tehran is now likely to focus on building leverage against Washington before agreeing to talks.
That includes by continuing to scale up its nuclear program. Iran is restarting some nuclear activity it previously agreed to suspend under a 2015 accord with world powers. Trump pulled the U.S. out of the deal last May and restored wide-ranging economic sanctions on Iran, setting in motion a year of steadily escalating tension with the Islamic Republic.
The U.S. sanctions are seen by Tehran as economic warfare aimed at regime change, and that presents an obstacle to coaxing Iran to the negotiating table, says Helima Croft, global head of commodity strategy at RBC Capital Markets.
"If we're going to persist down the policy course we're on, which is essentially to eviscerate the Iranian economy, even if we say we want to talk, are they going to listen to us unless we sweeten the offer?" she said.
She added, "It doesn't look at this point like we're really incentivizing them to sit down with us."
In order to reach a diplomatic breakthrough, Croft believes the Trump administration likely needs to revisit a list of 12 demands it placed on Iran last year. Those include stopping ballistic missile tests, accepting a tougher nuclear deal and ending support for U.S.-designated terror groups.
That could mean challenging hardliners, particularly National Security Advisor John Bolton, the official behind many of the recent U.S. escalations in recent weeks.
Trump has reportedly grown frustrated with Bolton over his role in increasing tension in the Middle East, but the president also tried to tamp down reports of conflict in the Oval Office. On Twitter, he called reports of "infighting with respect to my strong policy in the Middle East" fake news.
Eurasia Group's Rome and Wright say there's merit to those reports.
"Trump likely views Bolton as trying to box him in and limit options to avert violent confrontation," they said. "While Bolton's job is not likely in danger, the disagreements between the two men on this issue are significant and real."