President-elect Donald J. Trump on Tuesday refused to rule out using military force to retake the Panama Canal, which was returned by the U.S. to that country’s control decades ago.

Last month, Mr. Trump falsely accused Panama of allowing Chinese soldiers to control the vital shipping route, which connects the Atlantic and Pacific Oceans, and of overcharging American ships.

He has also claimed Panama charges U.S. vessels “exorbitant prices,” and warned that if they are not reduced after he takes office next month, he will demand that the United States be granted control of the canal “in full, quickly and without question.”

While it is unclear what prompted Mr. Trump’s recent obsession with the Panama Canal, some Republicans have long objected to a decades-old treaty that turned the shipping lane over to Panamanian control. When Ronald Reagan ran for president, he said the people of the United States were the canal’s “rightful owners” and brought audiences to their feet with the line: “We bought it; we paid for it; we built it.”

After a failed attempt by the French to construct a canal, it was ultimately built by the United States between 1904 and 1914. And the U.S. government managed the canal for several decades.

The U.S. also played a role in the creation of the state of Panama. At the beginning of the 20th century, the isthmus of Panama was part of Colombia. When Colombia rejected a proposed canal treaty, the U.S. government encouraged a rebellion. Colombia’s northern provinces eagerly seceded, forming the Republic of Panama. The United States Navy then kept Colombian troops from suppressing the rebellion.

U.S. control of the canal created significant tensions with Panama. In 1964, anti-American riots broke out in the U.S.-controlled canal zone.

The riots led to the renegotiation of the Panama Canal treaties. In 1977, U.S. President Jimmy Carter and the Panamanian leader Omar Efraín Torrijos signed the Torrijos-Carter Treaties. The agreements guaranteed the permanent neutrality of the Panama Canal. After a period of joint custody, the treaties called for the United States to relinquish control over the canal by the year 2000.

Panama took full control in 1999, and has since operated the canal through the Panama Canal Authority.

Mr. Carter, who died on Dec. 29, always considered the treaties to be signature achievements, and they figured prominently in his obituary.

“Through a bizarre accident of timing, we now have one president fantasizing about taking back the canal at just the time the world recognizes the canal transfer as an important part of a late president’s legacy,” said James Fallows, who was Mr. Carter’s speechwriter at the time and accompanied the president on that 1978 trip to Panama.

How has Panama responded?

In a statement of rebuke to Mr. Trump last month, President José Raúl Mulino of Panama wrote “every square meter of the Panama Canal and its adjacent area belong to PANAMA.”

Mr. Mulino also said U.S. vessels are not being overcharged. Rates being charged to ships and naval vessels, he insisted, are “not on a whim.”

Panamanian officials said all countries are subject to the same fees, though they would differ based on ship size. They are established in public meetings by the Panama Canal Authority, and take into account market conditions, international competition, operating and maintenance costs, Mr. Mulino said.

Rates have gone up recently, however. That’s because starting in 2023, Panama experienced severe drought, driven by a combination of El Niño and climate change, which Mr. Trump has called a hoax. With water levels at Gatun Lake, the principal hydrological reserve for the canal, at historically low levels, authorities reduced shipping through the canal to conserve the lake’s fresh water.

A Trump spokeswoman said that because the United States is the biggest user of the canal, the increase in fees hits its ships the most.

Chinese soldiers are not, as Mr. Trump has claimed, “operating” the Panama Canal.

“There are no Chinese soldiers in the canal, for the love of God,” Mr. Mulino said in a speech Thursday. “The world is free to visit the canal.”

A Hong Kong-based firm, CK Hutchison Holdings, does manage two ports at the canal’s entrances. And some experts have said that does raise valid competitive and security concerns for the United States.

Ryan C. Berg, the director of the Americas program at the Center for Strategic and International Studies, a Washington think tank, noted that CK Hutchison would likely have data on all ships coming through the Panama Canal. China has been using its shipping and maritime operations to gather foreign intelligence and conduct espionage.

“China exercises, or could exercise, a certain element of control even absent some military conflagration,” Mr. Berg said. “I think there is reason to be worried.”

Mao Ning, a spokeswoman for the Chinese foreign ministry, said Tuesday that China “will as always respect Panama’s sovereignty” over the Panama Canal.

China is the second-largest user of the Panama Canal after the United States. In 2017, Panama cut diplomatic ties with Taiwan and recognized the island as part of China, a major win for Beijing.

Can the United States reassert control?

Not easily.

Mr. Mulino has made clear the Panama Canal is not for sale. He noted that the treaties established permanent neutrality of the canal and “guaranteeing its open and safe operation for all nations.” And the Senate ratified the Panama Canal treaties in 1978.

Mick Mulvaney, Mr. Trump’s former chief of staff, suggested that the provocations were merely part of a negotiating tactic to get rates down.

“You know, I don’t envision American troops going in to retake the canal, but you got to think that someone is out there scratching their head going, ‘Is Donald Trump crazy enough to do something like that?’” Mr. Mulvaney said Tuesday on “The Hill” on NewsNation.

Mr. Berg said the neutrality agreement made it unlikely that Panama would even be able to grant special rates to the United States. And, he noted, Mr. Mulino is “incredibly pro-American” and likely eager to help the incoming Trump administration deal with issues like illegal immigration.

“President Mulino is going to be a great ally with the United States,” Mr. Berg said. “We should not want this to devolve into some kind of political fight because we’re going to need President Mulino on a number of other issues.”

But there is, as Mr. Trump has threatened, a military option. Mr. Trump could as president order an invasion of Panama. Under the terms of its constitution, Panama has no army. But experts dismissed Mr. Trump’s threat on Tuesday as empty intimidation.

“If the U.S. wanted to flout international law and act like Vladimir Putin, the U.S. could invade Panama and recover the canal,” said Benjamin Gedan, director of the Wilson Center’s Latin America Program in Washington. “No one would see it as a legitimate act, and it would bring not only grievous damage to their image, but instability to the canal.”