* Prosecution seeks three-year terms over church protest
* Defendants say they are "good people, friendly people"
* Putin said trio should not to be judged too harshly
By Maria Tsvetkova
MOSCOW, Aug 7 (Reuters) - A state prosecutor on Tuesday demanded a three-year jail term for three women from punk band Pussy Riot, saying they had abused God when they burst into a Moscow cathedral and sang a "protest prayer" against the Russian Orthodox Church's close links to Vladimir Putin.
The protest performed on the cathedral altar, which led to the three being charged with hooliganism motivated by religious hatred, outraged many Russian Orthodox believers.
But the case has caused an international outcry and focused attention on a crackdown on dissent since Putin returned to the presidency for a six-year term on May 7.
The European Union accused Russia on Tuesday of intimidation of judges and witnesses in the trial, and said the case breached international judicial standards.
Federal prosecutor Alexei Nikiforov dismissed the women's argument that their protest was not intended to offend believers and was aimed at highlighting the church's support for Putin.
"Using swear words in a church is an abuse of God," he said in closing arguments, watched by the women's lawyers, family and friends, packed into a tiny Moscow court. "The insult is not to Putin but to the social group of Orthodox Christian believers."
He said the actions clearly showed religious hatred and enmity and, deriding them as feminists who should be isolated from society, he added: "There was real mockery and humiliation directed at the people in the church."
Nikiforov did not press the court for the maximum seven-year sentence. Putin said last week that Maria Alyokhina, 24, Nadezhda Tolokonnikova, 22, and Yekaterina Samutsevich, 29, had done "nothing good" but should not be judged too harshly.
But the prosecutor ignored pleas by the opposition and human rights groups not to seek jail terms over the profanity-laced protest, when the trio, wearing bright balaclavas and short dresses, burst into Christ the Saviour Cathedral in February and belted out a song urging the Virgin Mary to rid Russia of Putin.
Pussy Riot, an all-women group, formed last October in protest against Putin's domination of Russia and his plan, now fulfilled, to return to the Kremlin. He could also seek another six-year term as president when his latest stint ends in 2018.
The defendants looked pale and tired as they sat silently in a metal and glass courtroom cage, two of them scribbling notes as they listened, before their turn came to address the court.
"I have the impression that we have not been listened to throughout the whole trial," said Tolokonnikova, her hair tied back with a flowered bandana, sounding confident and unbowed.
"WE ARE JESTERS"
"If we had put on dark balaclavas, someone could have mistaken us for bad people. But we are good people, friendly people who bring goodness and friendliness to the world ... We are jesters, clowns, maybe fools. We don't accept evil being done to anyone."
Defence lawyer Violetta Volkova said a jail sentence would be disproportionate and said: "These women are not here because they danced in a church. They are here because of their political beliefs."
The band members see themselves as part of a protest movement that last winter organised the biggest demonstrations since former KGB spy Putin first rose to power in 2000, at times attracting crowds in Moscow of 100,000.
"This is a nightmare. Blood is pouring from my ears," defence lawyer Nikolai Polozov said in a message on a social network site after the prosecutor's demand for jail terms.
In a country where few believe in the independence of the judiciary, the Kremlin could hope to win support among some of its critics if the sentences are relatively lenient. But this could offend church leaders demanding tough sentences. It is not clear when sentence will be passed but it could be this week.
A spokesman for EU foreign policy chief Catherine Ashton said Union officials were watching the trial closely.
"The EU is concerned about the reported irregularities related to this case," he said. "We are also worried by the reports of increasing intimidation, with pressure put on lawyers, on journalists and on possible witnesses."
Russian federal investigators said they had not received any official complaints about irregularities but that if they did, they would look into them.
The trio's protest also took aim at Patriarch Kirill, the head of the Russian Orthodox Church, and infuriated church leaders who have described Putin's 12-year rule as a "miracle of God" and described the women as doing the work of the devil.
The protest upset Orthodox Christian believers for whom the Christ the Saviour Cathedral is a sacred place of worship and its pulpit a place reserved exclusively for priests.
The case has provided Putin, 59, with a chance to deepen his contacts with the Russian Orthodox Church, which has enjoyed a surge in support since the Soviet Union collapsed in 1991.
But the case has also angered many Russians, including some believers, who see the reaction of the state and church as disproportionate. A sentence that is seen by the public as too harsh would risk backfiring on the president and the clergy.
Opposition leaders say the trial is part of a wider crackdown intended to silence Putin's critics and which also includes tightening checks on foreign-funded lobby groups, new controls on the Internet and big fines for protesters.