Cuban police have detained at least three leading dissidents ahead of a planned free-speech demonstration in the Plaza de la Revolución.

The arrests of Antonio Rodiles, Eliezer Avila and Reinaldo Escobar look set to be the biggest test yet of diplomatic relations with the US since they were restored earlier this month after 53 years of tension.

The crackdown came around lunchtime on Tuesday, just hours before local performance artist Tania Bruguera was due to stage an open-microphone event in Havana’s most politically sensitive square.

Police had denied Bruguera a permit for the “Yo tambien exijo,” [I also demand]” demonstration and warned activists not to participate, but several had indicated their willingness to participate in this test case for public dissent.

The authorities did not give them a chance.

Blogger Yoani Sanchez reported that her husband, Escobar – a senior editor of a dissident website 14ymedio.com – and Avila, the leader of the opposition group Somos Mas, were detained.

“They are taking away my husband @rescobarcasas and @eliecer_cuba in a police patrol car, handcuffed,” Sanchez tweeted.

#Cuba Se llevan a mi esposo @rescobarcasas y a @eliecer_cuba en una patrulla policial esposados — Yoani Sánchez (@yoanisanchez) December 30, 2014

Sanchez was later said to be held at home by police. She had earlier posted a message of support for Bruguera, saying she had spoken to the artist and told her that the performance had already succeeded in revealing the censorship in Cuba.

Police also detained Rodiles, the head of Citizen Demand for Another Cuba, a group that expressed support for the open microphone demonstration.

“I’ve been arrested,” he told the Associated Press by telephone as police took him away around 12:30pm.

Prominent Cuban dissident and blogger Yoani Sanchez, right, with her husband, Reinaldo Escobar, in Havana in 2013. Photograph: Desmond Boylan/Reuters

The Guardian was unable to reach other leading dissidents, though it was unclear whether this was connected to the police action.

About a dozen of them had earlier expressed opposition to the resumption of diplomatic relations, saying the US had prematurely eased pressure on the government of Raúl Castro without securing any concessions on human rights.

But the authorities took a low-key approach in the first week after the 17 December announcement of improved ties. At the weekly silent protest march four days later by the Damas de Blanco protest movement, there were none of the usual arrests and violence.

Bruguera’s planned “participatory performance” would, however, have been more of a challenge. She planned to give anyone a one-minute platform to discuss their views of Cuba’s future outside the government headquarters near the site where Fidel Castro used to give lengthy speeches to audiences of hundreds of thousands of people.