President Barak Obama touched down in Cuba on Sunday, becoming the first American leader to visit in nearly nine decades. His trip, the result of a stunning policy reversal 15 months ago, holds the potential to forge closer ties between longtime adversaries and exorcise one of the last ghosts of the Cold War.

The New York Times reports that just hours before Air Force One arrived at José Martí International Airport, however, the challenges of working more closely with Cuba became apparent as police officers, surrounded by pro-government demonstrators, detained dozens of protesters at a weekly march of the Ladies in White, a prominent dissident group.

The protest, which occurs on most Sundays outside a church in the Miramar district of Havana, was widely expected to be a test of Cuba’s tolerance for dissent during Mr. Obama’s trip. The arrests confirmed that the government was maintaining and intensifying its repressive tactics ahead of the visit.

“We thought there would be a truce, but it wasn’t to be,” said Elizardo Sánchez, who runs the Cuban Commission on Human Rights and National Reconciliation, noting that the arrests took place “in the moment that Obama was flying in the air to Cuba.”

The question of how to handle political opposition to President Raùl Castro’s government is one of many political thickets that Mr. Obama will have to navigate here.

It’s a land of endless waiting and palpable erosion. Yet after all these decades, an uncanny openness among the Cuban people remains.

Berta Soler, the head of the Ladies in White, is one of a dozen dissidents invited to meet with Mr. Obama on Tuesday at the United States Embassy. Other dissidents said, however, that it was not clear if she would attend because of her opposition to the American president’s policy of engagement.

Mr. Obama also arrives with a great deal of support for his effort to bring old enemies together, both among the Cuban people, who describe Mr. Obama as a transformative figure, and within the United States, where interest in Cuba has already begun to swell.

The president, who arrived with the first lady, Michelle Obama; their daughters, Sasha and Malia; and his mother-in-law, Marian Robinson, will begin and end his trip as a tourist in chief. He planned to stroll through Old Havana on Sunday and attend an exhibition baseball game between an American major-league team and Cuban players on Tuesday.

In between, his itinerary is shaped by the contradictions that still complicate the United States’ relationship with Cuba: a meeting on Monday with Mr. Castro at the Palace of the Revolution, the seat of the Communist government, and another on Tuesday with the group of dissidents who have been victims of government repression.