WASHINGTON—After moving to the precipice of military action against Iran, President Trump finds himself caught between negotiations that show few signs of yielding a nuclear deal and a war he is reluctant to join.

By deferring a decision on a military strike , Trump’s calculation is that Israel’s continued blows against Iran’s nuclear infrastructure or Tehran’s capitulation at the negotiating table might deliver the outcome he has long sought: an end to Iran’s uranium enrichment.

The risk is that Iran concludes that Trump is bluffing, opts to endure Israel’s bombs and clings to its longstanding position that it has the right to an enrichment program.

Then Trump would face enormous pressure to order an attack against a foe that, though already battered by Israel, retains several options for striking back at the U.S. and its allies.

Since beginning his second term as president, Trump has been adamant that Iran can’t enrich uranium, a capability that Tehran insists is for peaceful purposes but that is also an essential component of a nuclear bomb.

At the same time, Trump has sought to avoid a Middle East war that many of his supporters fear could drag American forces into an open-ended conflict, no matter how much damage the U.S. and Israel inflict on Iran’s nuclear sites.

Dennis Ross , who served as a senior official on Middle East issues in Democratic and Republican administrations, said that for Trump’s gambit to work, Tehran needed to have no doubt Trump is prepared to use force and isn’t bluffing.

“There ought to be very clear messages to the Iranians that the president is giving one last time frame for diplomacy,” Ross said. “Here are the conditions that would prevent him from acting militarily.”

Asked Friday if the Iran crisis reminded him of Iraq in 2003, when President George W. Bush went to war claiming it was necessary to halt Saddam Hussein’s weapons programs, Trump said no.

“There were no weapons of mass destruction,” he said of Iraq. But with Iran in “a matter of weeks, or certainly within a matter of months, they were going to be able to have a nuclear weapon,” he added. “We can’t let that happen.”

He dismissed an assessment by Director of National Intelligence Tulsi Gabbard in March that Iran hadn’t made a decision to build a nuclear weapon. After being criticized by Trump, she said there was no disagreement between them.

In addition, Trump said he isn’t planning to use U.S. ground troops if he orders American military action.

Tehran told diplomats in several conversations this past week that it wouldn’t end its enrichment of nuclear fuel and wouldn’t enter talks with the U.S. unless Israel stops its attacks, said Arab and European officials.

The most effective way to take out Iran’s heavily defended Fordow nuclear-enrichment site, which is buried in a mountain, is with massive ground-penetrating bombs carried by U.S. B-2 bombers, according to experts. Trump told aides this past week that he had approved attack plans , but held off giving the final order to see if Tehran would abandon its nuclear program.

Israel, according to analysts, might feel compelled to move ahead soon with its own military operation against the Fordow site out of concern that Trump might never approve a U.S. strike, even though an Israeli action might be riskier and more challenging.

If Israel fails to effectively damage the site in the coming days, Trump will face even more pressure to intervene, while Iran’s leaders would have less reason to accede to his demands.

Trump has been clear about his goal of denying Iran a nuclear weapon but less so about taking military action.

He left the Group of Seven meeting a day early, saying he had to rush back for a National Security Council meeting Tuesday on how to bring about a “real end” to Iran’s nuclear program. Trump two days later put an additional two weeks on the clock.

Despite the mixed signals from Trump, Iranian leaders are almost certainly factoring into their decision-making that the U.S. president has taken direct action against them before, targeting one of their top commanders by ordering a drone attack on Maj. Gen. Qassem Soleimani in Iraq in January 2020.

Yet Trump pulled back from a retaliatory strike against a target on Iranian territory out of fear that it would result in too many casualties after Iran shot down a U.S. drone in 2019.

Politically, the two-week pause might make it easier for the president to straddle the divisions between his Republican supporters, who have been torn over the prospects of U.S. military action.

Sen. Lindsey Graham (R., S.C.) has urged Trump to act militarily to end Iran’s nuclear program, saying on Fox News that Trump “will, at the end of the day, help Israel finish the job.” Steve Bannon , the former Trump adviser, has been skeptical of the case for U.S. military action, saying that “the Israelis have to finish what they started.”

Vice President JD Vance tried to bridge the gap between the isolationist and hawkish elements of the Republican Party in a recent social-media post, noting that “the president has shown remarkable restraint in keeping our military’s focus on protecting our troops and protecting our citizens.” Vance added, “He may decide he needs to take further action to end Iranian enrichment.”

In military terms, Trump’s move gives the U.S. military more time to deploy forces to the Middle East and prepare for an Iranian counterblow if Trump eventually opts to pull the trigger.

Israel’s continued strikes are likely to take a further toll on Iran’s missile launchers, meaning that the U.S. would confront a less capable Iranian military if it decides to join the Israeli military campaign.

“From our standpoint, it allows some time to make sure we are fully prepared,” said Joseph Votel , a retired Army general who led U.S. Central Command, which oversees American forces in the Middle East.

For the Iranians, said Trump, the U.S. pause gives them time “to come to their senses.”

Write to Michael R. Gordon at michael.gordon@wsj.com and Lara Seligman at lara.seligman@wsj.com