"I have recently written to my brother in Christ, the Primate of Uganda, Archbishop Stephen Kaziimba, to express my grief and dismay at the Church of Uganda's support for the Anti-Homosexuality Act," Archbishop of Canterbury Welby said in a statement.
"There is no justification for any province of the Anglican Communion to support such laws: not in our resolutions, not in our teachings, and not in the Gospel we share," Welby said in his statement.
Kaziimba said in May he was grateful for the new law. He said homosexuality was being forced on Uganda by "foreign actors ... who disguise themselves as human rights activists" and went against Ugandans' religious and cultural beliefs.
Welby said in Friday's statement he was deeply aware of the history of colonial rule in Uganda but "this is not about imposing Western values on our Ugandan Anglican sisters and brothers".
"It is about reminding them of the commitments we have made as Anglicans to treat every person with the care and respect they deserve as children of God," he said.
Under the law, approved by President Yoweri Museveni in May, gay sex is punishable by life in prison while "aggravated homosexuality," including transmitting HIV, attracts the death penalty.
The Ugandan church has been at the forefront of the Global Anglican Future Conference (GAFCON), a conservative group. In April, GAFCON said it no longer had confidence in Welby because of his comments in support of the blessing of same-sex unions in churches.
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