Two members of Russian protest group Pussy Riot have been denied asylum in Sweden, meaning the couple and their two young children could be deported back to their homeland.

Alexey Knedlyakovsky and Lusine Djanyan fled Russia last year because they said they were targeted and threatened by the country's security services for being prominent critics of President Vladimir Putin.

Earlier this year, NBC News traveled to the remote town where the couple and their young son were living as they waited for a decision on their asylum application. Since then they have had another child.

On Thursday, they learned their bid to remain in Sweden had been denied.

"We do not think, we are sure: We will be put in jail," Knedlyakovsky said of the prospect of being sent back to Russia. "This is a signal to all political activists in Russia that no one will defend them if something happens."

Pussy Riot is an artistic collective that gained worldwide notoriety for its punk-rock protests against Putin, Russia's clergy and the country's poor record on LGBT rights.

The couple participated in the group's demonstration at the 2014 Winter Olympics in the Russian city of Sochi.

They were beaten, pepper-sprayed and whipped by members of an ultranationalist Russian militia known as the Cossacks. Knedlyakovsky was left with blood streaming down his face after he says he was hit over the head with his own guitar.

The pair also said they were repeatedly harassed, detained and beaten by Russian security services in an attempt to pressure them into silence.

"We were not given the opportunity to live normally," Djanyan told NBC News in February.

After they fled the country, another Pussy Riot member claimed he was poisoned after he and others ran onto the field during the soccer World Cup final in Moscow this summer.

Under Putin, Russia has increasingly cracked down on political opponents and human-rights campaigners, according to independent watchdogs.

The Swedish Migration Board confirmed that Knedlyakovsky and Djanyan's asylum application had been denied but said it wasn't able to give details because of privacy rules.

Knedlyakovsky said the board dismissed their claims that they were at risk, and that it ruled any punishment faced by Pussy Riot members was "proportionate." But he called that decision "a manipulation of facts."

"The Swedish immigration system messed up," Knedlyakovsky said. "Sweden believes that the participants of Pussy Riot are not subject to political persecution in Russia."

Alexey Knedlyakovsky and Lusine Djanyan with their two children at the Migration office in Lindesberg, Sweden, on Thursday. Elin Jonsson

The couple will appeal the decision in court. If that fails, they will be asked to leave Sweden, and forcefully deported by the police if they don't go willingly.

"We consider all options except return," Knedlyakovsky said, "because the return is a direct way to prison and to physical violence against us."