All three members of Russian punk band Pussy Riot have pleaded not guilty to charges of hooliganism over an anti-Vladimir Putin protest at Moscow's main cathedral.
The women were taken into custody in February after the protest at Moscow's Christ the Saviour Cathedral.
The case has divided Russia and inflamed the religious establishment, correspondents say.
The song outraged the Russian Orthodox Church. It accused them of blasphemy.
Supporters say the case reflects the state's growing intolerance of government opponents.
In a written statement, band member Mariya Alekhina said the performance was an administrative offence, but had become a criminal case "as a result of the influence of political, law-enforcement and spiritual elites".
At the start of the trial, the three women, Nadezhda Tolokonnikova, Ms Alekhina and Yekaterina Samutsevich, were led into court in handcuffs, and locked into a cage of bullet-proof glass.
In court, Ms Tolokonnikova said that although they were pleading not guilty, that did not mean they were not prepared to apologise for the pain their performance in the cathedral had caused.
They each stood up and answered a series of questions from the judge in turn, which included their educational level, citizenship and the birth dates of their children.
The women are facing the charge of hooliganism motivated by religious hatred or hostility and could face up to seven years in prison.
In an interview with UK newspaper The Times, which was also broadcast on Russian TV, Russian Prime Minister Dmitry Medvedev has said it is up to the court to decide whether the women have committed a crime.
"This case is a high-profile one because it really is about our understanding of the rights and freedoms of an individual.
"However, there will always be differences in the perception of what is permitted and what is not permitted from a moral point of view and of where moral misdemeanours transform into criminal offences."
The women caused outrage when they stormed on to the altar of Christ the Saviour Cathedral, and sang an obscenity-laced song that implored the Virgin Mary to "throw Putin out".
The head of the Russian Orthodox Church, Patriarch Kirill, has said the act amounted to blasphemy.
The case has divided Russia, with many feeling the women have been too harshly treated, and are being made an example of as part of attempts to clamp down on the opposition, the BBC's Daniel Sandford reports from the court.
Two of the women have young children, and all three have repeatedly been denied requests to be given bail while awaiting trial.
Pussy Riot made headlines around the world late last year when footage of their controversial public performances at Moscow landmarks such as Red Square attracted millions of viewers on the internet.
More than 100 prominent Russian actors, directors and musicians have urged the authorities to release the three.
Western musicians such as Sting and the Red Hot Chili Peppers have also criticised the women's arrest.
Activists have said the case indicates that President Putin, now serving a third term in office, is not heeding calls for him to be more tolerant of political opponents.