WASHINGTON—President Trump has told associates in recent days that he wants to avoid a protracted war in Iran and that he hopes to bring the conflict to an end in the coming weeks.

Nearly one month into the war, the president has privately informed advisers he thinks the conflict is in its final stages, urging them to stick to the four-to-six-week timeline he has outlined publicly, according to people familiar with the matter. White House officials planned a mid-May summit with Chinese leader Xi Jinping in Beijing with the expectation that the war would be concluded before the meeting begins, some of the people said.

The problem is Trump has no easy options for ending the war, and peace negotiations are at a nascent stage.

In discussions with outside political allies, his attention has at times shifted to other topics, including the coming midterm elections, as well as his decision to send immigration agents to airports and strategies to move legislation to tighten voter-eligibility rules through Congress. Trump told an associate that the war was distracting from his other priorities, one of the people said.

The president appears ready to shift to his next big challenge, another person who spoke to him recently said, though Trump didn’t say what that might be. Some allies are hopeful he can pivot to ousting the communist regime in Cuba, while close advisers want him to focus on the most pressing issue facing voters: concerns about the cost of living, which have been exacerbated by the war.

“President Trump is extraordinarily skilled at multi-tasking and works on multiple challenges at the same time,” White House press secretary Karoline Leavitt said. “The President is laser focused on fully achieving the military objectives against the terrorist Iranian regime. The president’s sole focus is always victory.”

Trump this week signaled renewed interest in reaching a diplomatic settlement to end the conflict, walking back a weekend threat to strike Iran’s power plants. Middle Eastern intermediaries have traded opening proposals from Tehran and Washington, and U.S. officials have said they are open to further discussions in the coming days. At the same time, the U.S. is turning up the heat on Iran, deploying additional troops to the Middle East.

One idea that Trump has floated to advisers: securing U.S. access to some of Iran’s oil as part of any deal to end the war, according to a senior administration official. The official said there isn’t any current planning under way for that outcome.

The U.S. will hit Iran “harder than they have ever been hit before” if Tehran doesn’t make an agreement to end the conflict, Leavitt told reporters Wednesday. “President Trump does not bluff and he is prepared to unleash hell.”

Trump is willing to order U.S. troops on Iranian soil, but is reluctant to do so, in part because it could upend his goal of a speedier end to the conflict. He is concerned that the number of U.S. troops killed or injured in the operation could rise if the war continues, U.S. officials said. So far, nearly 300 Americans have been wounded, and 13 have been killed.

People close to the president cautioned that it is often difficult to predict what decisions Trump might make about the war, noting that as the conflict has unfolded, he has vacillated behind the scenes between embracing diplomacy and ramping up strikes. Some people close to Trump are urging him to go harder, saying regime change in Iran could be legacy- defining.

Ending the war isn’t up to Trump alone. The U.S. and Iran are far from reaching an agreement to stop the fighting, and Tehran so far has rejected direct talks with Washington. Without a deal or a firm military victory, Trump is likely to face the continued blocking of the Strait of Hormuz, which would continue to roil the global energy market. Israel, which sees threats from Iran as existential, could continue its operations without the U.S. Gulf countries that have endured weeks of attacks are considering retaliation of their own.

Trump has directed the military to keep pressure on Tehran, according to a senior U.S. official. The Pentagon is deploying thousands of ground troops to the Middle East to give the president options. Once additional soldiers and Marines are in position, Trump could quickly order a targeted raid, either inside Iran itself or on one of the islands along its southern coast.

“We see ourselves as part of this negotiation as well,” Defense Secretary Pete Hegseth said Tuesday at an event with Trump. “We negotiate with bombs.”

Trump said earlier this week that Hegseth and Gen. Dan Caine, the chairman of the Joint Chiefs of Staff, were “quite disappointed” by the prospect that the war could be over soon. “They were not interested in settlement, they were interested in just winning this thing,” Trump said.

Trump has for weeks sought to characterize the war as a temporary distraction, emboldened by January’s swift military operation in Venezuela. He has called the conflict an “excursion” and a “military operation.”

“This war has been won. The only one that likes to keep it going is the fake news,” Trump said Tuesday, amplifying his private complaints about media coverage of the operation. Trump has also sought to push the burden onto allies, imploring them to take charge of untangling the Strait of Hormuz, a critical oil corridor.

Meanwhile, in the U.S., the political landscape for Republicans is difficult going into the midterms. On Tuesday, a Democrat flipped a South Florida state-legislative seat that includes Trump’s Mar-a-Lago estate.

Republicans worry the war could worsen their political problems, as high costs and Trump’s poor approval numbers weigh down candidates in key statewide races.

As he contends with the war, Trump has taken time to tend to political matters.

On Friday, he strode into the Mar-a-Lago ballroom to cheers of “U.S.A.” from local Republicans gathered for a $1,200 per-person fundraising gala.

“I didn’t know I was going to be here today,” Trump said. “I am supposed to be prosecuting the war, but the war’s going very well.”

Write to Annie Linskey at annie.linskey@wsj.com, Alexander Ward at alex.ward@wsj.com and Alex Leary at alex.leary@wsj.com