The head of Uganda's Anglican Church said on Wednesday that Justin Welby, who has resigned as Archbishop of Canterbury, had split the global Anglican communion.

Stepping down as the spiritual leader of Anglicans worldwide on Tuesday, Welby said he had failed to ensure a proper investigation into allegations of abuse by a volunteer at Christian summer camps decades ago.

The Church of Uganda has long been at loggerheads with the Church of England on its stance on homosexuality, and said last year it no longer had confidence in Welby.

The Church of Uganda stopped recognising Welby's authority over his "inability to uphold the historic and Biblical teaching of the Church of England on marriage and family," Ugandan Archbishop Stephen Kaziimba said in Wednesday's statement.

"Unfortunately, this is the same compromised leadership that has led to the fabric of the Anglican Communion being torn at its deepest level," he said.

Welby, who had spent years trying to prevent the global Anglican communion fracturing, had faced calls to quit after a report last week found he had taken insufficient action to stop one of the Church's most prolific serial abusers.

"It grieves us deeply that so many people suffered from the continued abuse of John Smyth over many years simply because the church's leadership covered up the abuse, did not uphold the moral teaching of the Bible and the church, and failed to defend the vulnerable," Kaziimba said in the statement.

Kaziimba supported Uganda's strict anti-homosexuality law that was passed last year and which imposes tough penalties including death for some same-sex acts.

He said homosexuality was being forced on Uganda by foreign agents who disguised themselves as human rights activists.

His stance drew a rebuke from Welby who wrote to the Church of Uganda urging it not to support the law.

Around 36% of Uganda's population of around 46 million are Anglicans. Catholics form the majority religious denomination in the east African country.

The anti-homosexuality legislation has wide support in Uganda but has drawn criticism in the West and the United States has imposed sanctions including travel bans.