The Jordanian prime minster is under pressure to resign after a Christian anti-Islamist writer was shot dead outside a court room where he was due to stand trial on Sunday.

On Monday around 300 supporters of Nahed Hattar, the individual who was killed, protested outside prime minister Hani Mulki's office in Amman and demanded he quit. Human rights organisations condemned the killing as "deplorable" and "senseless".

Hattar's family, who are Christians, have refused to collect the 56-year-old's body for burial, saying they won't until action is taken against those who incited violence.

"We demand that all those whose actions lead to the assassination of the martyr be held accountable," Hattar's brother told AFP.

Hattar was arrested in August after he shared a satirical image on Facebook that showed God's face – a highly offensive act in Islamic cultures. The cartoon entitled 'In Heaven' showed a bearded jihadi fighter in bed with two women ordering God to bring him wine and clear up the dishes.

He was charged with "inciting sectarian strife" and publishing material that insults "other people's religious feelings" under articles 150 and 278 of Jordan's penal code. The charges can carry sentences of up to three years in prison.

After he was bailed on September 8, he was shot at close range as he entered the Jordanian court of justice for his trial on Sunday.

His family said he was given no protection despite receiving hundreds of threats. They added his death could have been prevented if Mulki had not ordered an investigation into the sharing of the image.

"The prime minister should have left it to the judiciary," said Mary Hattar, one of Hattar's cousins. "He asked for protection but when he was released from prison he was asked to sign a document [stating] that he was responsible for his own safety," she added according to local media.

One of Hattar's brothers, Khaled, told AFP: "We handed over 200 names [of people who had threatened the writer] to the governor [of Amman], including that of the assassin, and demanded protection.

"But he refused, saying there was 'no real threat'."

A spokesman for Amnesty International described Hattar's death as "deplorable" and said the fact he was even standing trial in the first place is an "alarming attack on freedom of expression".

The charity's Middle East and North Africa research and advocacy director Philip Luther said: "By using strict blasphemy laws to prosecute a person for peacefully exercising their right to freedom of expression, the Jordanian authorities are fuelling a climate in which violent threats against people whose views are deemed offensive by others are allowed to flourish."

Sarah Leah Whitson, Middle East director at Human Rights Watch, agreed and said the "senseless murder in front of an Amman courthouse comes on the heels of the government's senseless charges against him over a cartoon he posted to his Facebook page".

She went on: "Jordanian authorities should recognize that 'defamation of religion' laws and prosecutions effectively contribute to violent extremism.

"The government should immediately suspend prosecutions for defamation of religion, move to repeal the provisions from its penal code, and allow citizens to engage in peaceful debate even of 'taboo' subjects."