INDORE, INDIA (REUTERS) - Naveen Gadke was arrested on April 20 and charged with the rape and murder of a baby girl in central India.

Three weeks later, a court sentenced the 26-year-old odd-job man to death in the fastest such trial known to have happened in modern India, a nation where public outrage is running high because of a series of rapes and related killings.

Police, prosecutors and the district court in the city of Indore worked at a furious pace to get the conviction quickly, amid a backlash on the streets, including marches in this city of about 2 million, 550 miles (885km) south of Delhi.

This is in a country where Prime Minister Narendra Modi's government last month (April) introduced the death penalty for rapes of girls under 12 years in response to public pressure but which has a notoriously slow court system, with cases taking at least six years on average to final ruling, according to governance tracking group Daksh.

But the pace of the trial, the intensifying push for speedy hearings in rape cases, and questions about the legal defence provided to Gadke - who pleaded not guilty - have raised concerns among some legal rights advocates.

They are fearful there will be wrongful convictions and hangings when a defendant cannot afford to hire a good lawyer.

"While expeditious trials are ideal, these should not be at the cost of fair trial safeguards like the right to adequate time to prepare a defence and the presumption of innocence,"said Ms Leah Verghese, senior campaigner at human rights group Amnesty International India, in an e-mail response to questions.

Senior Supreme Court lawyer Rebecca John said she was concerned. "As a principle, I am opposed to rushing through investigative processes and trial processes" she said.

But reflecting the mood of the nation, well-known Supreme Court lawyer Dushyant Dave, a vocal supporter of capital punishment, said India "needs to send at least 500 people to death in the next one year to end this endemic" of rape.

"Our system is archaic and extremely inefficient," he added.

Such views have resonated with the mother of the dead three-month-old girl as she sat on the front yard of a 200-year-old palace where her homeless family sleeps in the open.

She told Reuters she was happy with the swift verdict but her daughter would get justice only when Gadke is hung to death, just as quickly.

"Once such men are hanged, no one will dare to do anything like this to any girl," she said.

Rape victims and their families cannot be identified under Indian law.

Gadke could not be contacted as journalists are not allowed to speak with convicts in jail as per a home ministry directive. Mr Sachin Verma, Gadke's lawyer, said his client told him that his estranged wife framed him, but said little else.

Reuters could not trace Gadke's wife to seek comment.

At trial, the mother, police officers and the prosecution lawyer said security cameras showed Gadke taking away the infant as she lay asleep by her parents. Fifteen minutes later, he was seen coming out of the basement of a nearby building, where her blood-smeared body was found, police said.

Medical tests, completed quickly under instructions from government officials, confirmed she was raped, and the semen from a vaginal swab was found to be a DNA match with Gadke, according to court documents reviewed by Reuters.

Gadke's lawyer, who specialises in matters related to crimes against children, said he reluctantly took the case on state government orders.

That was after four other lawyers refused to defend Gadke, Mr Verma said. In a sign of how high temperatures were rising in the community, around a dozen lawyers attacked the defendant outside the court when he first arrived, slapping and shoving him, according to police.

Prosecutors presented 29 witnesses, including police and shopkeepers who found the victim's body, and "everybody supported the prosecution", said Mr Verma. He presented no witnesses for Gadke's defence.

Mr Verma said he could have done better if he had more time to prepare for the case.

"They had to create a story and they had to decide quickly,"said Mr Verma, who is expecting to receive 4,000 rupees (S$79) from the state government for representing Gadke.

"My client told me, 'Everyone has already decided I am guilty. What's the point of all this?'"

Special prosecutor Mohammad Akram Shaikh said that they had conclusive evidence against Gadke.

Judge Varsha Sharma, who deals with matters related to crimes against children and ruled on the case, declined to comment.

Police pressed charges against Gadke within seven days of the crime, said Police Inspector Shivpal Singh Kushwah.

"All of us wanted to send a message that the law can work fast, and we succeeded," he said.

The court sat for seven straight working days to hear the case, unusual in India where one court is often dipping in and out of several cases on the same day. A government-run laboratory conducted tests on forensic evidence within four days of a police request. This usually takes more than a month, Police Inspector Kushwah said.

After hearing details of his crime from Special Prosecutor Shaikh and the witnesses, Judge Sharma found Gadke guilty and ordered his death by hanging.

"This falls under the rarest of rare case and it would be appropriate to hand such a criminal the toughest punishment,"the judge declared.

The sentence has to be confirmed by a higher court, for which Gadke will be provided a different lawyer by the state government. The court's decision can be challenged in the Supreme Court. An appeal to India's president is the last resort. The entire process can take years.

Even before Gadke's trial, there were growing calls to speed up child rape trials.

Lower courts take an average of five years to complete cases of prisoners sentenced to death, high courts one year and four months, and the Supreme Court two years and one month, according to a 2016 report by the Centre on the Death Penalty in the National Law University of Delhi.

The university study found that 74 per cent of 373 death row prisoners they interviewed were economically vulnerable. The majority were from low castes and religious minorities. In the Indore case, Gadke did various jobs such as cleaning utensils in eateries.

By contrast, trials involving India's rich and powerful sometimes take more than 10 years. Gurmeet Ram Rahim, a wealthy self-styled godman who had many followers, was convicted last year on charges of raping two followers - 15 years after the case was registered.

Government statistics show that since 2012, when a young woman was gang raped in a moving bus in Delhi igniting national uproar, reported rape cases have climbed 60 per cent to around 40,000 in 2016 - about one every 15 minutes - with child rape accounting for about 40 per cent.