Religious scholars and legal experts accuse the al-Shabaab movement of committing crimes and carrying out executions under the "false pretext of implementing Islamic law".
Human rights organisations and activists also condemn al-Shabaab's tribunals in areas under its control. Rulings have been made without a fair trial and in violation of Somali and international laws, they say.
Courts run by al-Shabaab have issued sentences including execution, stoning, flogging and cutting off limbs. The al-Qaeda allied movement often warns people against co-operating with the Somali government, even for familial reasons, threatening execution.
Over the past three years, the al-Shabaab movement has executed dozens of men and women throughout the country on charges including aiding the Somali Transitional Federal Government (TFG) and the AU forces, or spying for neighbouring governments.
In mid-March, al-Shabaab fighters executed a young man in his early 20s in the Galgalato area north of Mogadishu on charges of spying for Somali government forces.
"The application of punishment is a matter for the legitimate state, and is not the right of any group, whether it elects to implement the death penalty or implements the hudud provisions," said Sheikh Abdulqadir Somow, spokesman for the Supreme Council of Ahlu Sunna Wal Jamaa scholars, part of the Federation of Sufi Orders in Somalia.
Sheikh Somow said al-Shabaab has committed crimes and murder against innocent civilians under the guise of spying charges. He said there is disagreement among Islamic jurists about judgements against people convicted of spying, but killing them is not endorsed by Islamic law.
"This group has committed more than a crime, and if you look at the way in which it is killing people, its actions have no legal cover, but are contrary to Islamic law," he told Sabahi. "The al-Shabaab group is seeking to terrorise Somali citizens with these rulings."
Somalis have been shocked by the movement's strict interpretation of Islamic law. The movement decapitated several people on charges of being Christians, spies or apostates of Islam. After the victims are executed, al-Shabaab members bury them in sites called "the infidels' cemeteries", residents of areas formerly occupied by al-Shabaab said.
Over the past three years, the al-Shabaab movement, which was in control of the city, conducted a series of terrifying operations that terrorised much of the city's population," said Omar Isaac, a 43-year-old resident of Baidoa, where allied forces recently gained control. "Baidoa was the scene of the largest execution operation. Elements of the al-Shabaab movement cut off the heads of seven city residents at one time on charges of being Christians and spies in June 2009."
Mohamed Hassan, a 36-year-old resident of Beledweyne in central Somalia, which allied forces took control of this year, said al-Shabaab committed numerous crimes against town residents, and their tactics against citizens reached the point of executing anyone they believed was co-operating with the transitional government or criticising the movement's policy.
"Al-Shabaab militants executed two teenage girls in Beledweyne in October 2010 on charges of spying for the pro-government forces, and that was the first execution of its kind to take place in the town," Hassan told Sabahi.
Hassan said a mass grave created by al-Shabaab was found in Beledweyne containing more than 20 bodies in January. "The corpses found in the mass grave included civilians the al-Shabaab movement killed without trial," he said.
Somow accused al-Shabaab of committing crimes against the Somali people under the false pretext of implementing Islamic law.
"The al-Shabaab group committed crimes in the name of Islam. It is unfortunate that the name of Islam is being used to kill innocent Muslims," he said.
Somow said al-Shabaab "does not have any legal validity to apply these provisions, and it does not have the right to issue judicial rulings because that is the jurisdiction of the official authorities".
Bashir Ahmed, a law professor and an administrator for a local justice watchdog association, said death sentences ordered by the al-Shabaab were issued during show trials that violated international legal standards and human rights.
"The executions carried out by the al-Shabaab movement were issued during show trials, and fair trials are usually not provided for the accused," Ahmed told Sabahi. "The convicted are not granted the right to appeal the ruling against them or challenge the judicial decisions to defend themselves."
He said that not allowing the defendants the right to appeal the judgment against them or defend themselves demonstrates the movement's complete disregard for human life.
Hassan Abdullahi, who works for a local human rights organisation, said al-Shabaab's methods include inviting people to watch executions, causing negative psychological repercussions on viewers, sowing fear rather than furthering justice.
"The Al-Shabaab movement displays severed body parts from the convicted in public squares and hangs them from electric poles so ordinary people can view them," Abdullahi said. "The executions and stonings are conducted in open areas in view of thousands of people who are invited to watch the proceedings as they are carried out."
Al-Shabaab militants force residents to watch the executions, stonings and floggings, he said, using loudspeakers to call people to watch.
"Al-Shabaab militants slaughter civilians and dump their bodies in the streets or markets, and in some cases the severed heads are tossed in the street and the rest of the bodies are left in another area not far from where the heads are thrown in order to terrorise the people and create panic in the hearts of citizens," he said.