French authorities have arrested a 24-year-old woman on suspicion of killing a 12-year-old girl whose body, covered in cuts and bruises, was found in a plastic suitcase outside her home in Paris. The death of the girl, named Lola, quickly became a source of political tension, with opposition parties seizing on the profile of the suspect – who had entered the country illegally – to call for tougher immigration policies. The Paris prosecutor’s office said the girl disappeared on Friday afternoon and her body was discovered that evening by a homeless man outside her building in the 19th arrondissement. She had been asphyxiated, prosecutors said. The main suspect was seen on CCTV exiting the building in the afternoon carrying heavy luggage, including the suitcase in which the victim was found. She was arrested on Monday and put under formal investigation on accusations of murder, rape and acts of torture, a judicial source said. Neighbours laid flowers and candles in tribute to the girl. “It’s unbearable,” said one, who declined to give her name. “We’ve been living in this neighbourhood for years and we’ve just come here to give support to the family, in leaving a bouquet, because like many people this breaks our hearts.” Another neighbour said: “Twelve years old … poor girl … it doesn’t make any sense.” The French president, Emmanuel Macron, met the girl’s parents. His office said he “offered them his condolences and assured them of all his solidarity and support in the ordeal they are going through and which upsets us all”. The far right and some in the conservatives’ ranks said the incident showed failings in the government’s law and order policies. “This murder should not have happened. The assassin should not have been in France,” said Olivier Marleix, the president of the conservative Les Républicains group in the national assembly. “There is a very deep emotion in our country.” The far-right leader Marine Le Pen said in parliament: “Too many crimes are being committed by clandestine immigrants one has not been able or willing to deport.” The prime minister, Élisabeth Borne, asked Le Pen to “show some decency”. Alexandre Silva, a lawyer representing the suspect, told BFM TV that he could not comment on the case. Newspapers, citing police and judicial sources, said the suspect was Algerian.