A Saudi anti-terror agency has argued that people who leave Islam should not be punished by death, sparking rumours the kingdom would abolish capital punishment for apostates.

An anti-terror unit in Saudi Arabia's defence ministry has argued that people who leave Islam should not be put to death, sparking rumours the kingdom would abolish capital punishment for apostates.

The Ideological Warfare Center [IWC] last Saturday published a series of online statements arguing that there was no death penalty for those deemed apostates under Islamic law, citing the Quranic and Islamic scholars.

In Saudi Arabia apostasy can be punishable by death.

"There has been much Islamic juristic debate both old and new about the penalty for apostasy. It is one of the many issues discussed and expanded on with false interpretations in a number of terrorist tracts," the IWC said on Twitter.

"It has not been proven that God's Prophet killed those who - by Quranic criteria - renounced their religion. His companions and followers, their followers and some Islamic scholars have taken a different approach," it said.

"Apostasy can be understood to be high treason as it can result in repercussions that infringe on 'public rights' in the form of communal harmony, the sanctity of the community's religion and safeguarding religion's reputation. When this happens it has important considerations that are reflected in criminal law," it added.

Saudi social media users were quick to interpret the IWC's message as a move towards abolishing the death penalty for people convicted of apostasy, with some praising the development and others condemning it.

The official Saudi Press Agency responded to the rumours, categorically denying the claims.

"Allegations published by some sources in good intention or otherwise that Saudi Arabia has embarked on abolishing the apostasy penalty are altogether false and incorrect," it said in a statement.

The controversy comes as Riyadh has said it wants to adopt a "moderate" state-sanctioned interpretation of Islam, with women recently being granted the right to drive.

In October, the kingdom said it would establish an authority to monitor interpretations of the Prophet Mohammed's teachings to prevent them being used to justify violence or terrorism.

Despite the efforts to modernise, senior Wahhabi clerics - who strongly influence the royal family - endorse execution by beheading for offences that include apostasy, adultery and sorcery. They also describe Shia Muslims as heretics.

Saudi activist Raif Badawi was arrested in 2012, and brought to court on several charges including apostasy and insulting Islam using electronic means.

He was sentenced to seven years in prison and 600 lashes.

Footage emerged in July of Badawi being flogged by authorities in a public square.