Justin Welby, the head of the Church of England and the worldwide Anglican Communion's 85 million members, said last week he had written to Ugandan Archbishop Stephen Kaziimba to express "grief and dismay" at Kaziimba's support for the law.
Issues of LGBTQ rights have sharply divided Anglicans, with the church's GAFCON coalition of conservative adherents among the most critical.
The statement by Mbanda, who is also the head of Rwanda's Anglican Church, mentioned but did not explicitly offer support for the Ugandan law.
Anglicans created GAFCON in 2008 in response to what the group says was certain Western churches' abandonment of bible-based orthodoxy.
The Church of Uganda says 36% of Uganda's population of around 45 million are Anglicans.
Persons:
Justin Welby, Stephen Kaziimba, Joe Biden, GAFCON, Laurent Mbanda, Mbanda, Welby, Archbishop Kaziimba, Philbert Girinema, George Obulutsa, John Stonestreet
Organizations:
Wednesday, of England, U.S, Anglican, Global, Thomson
Locations:
KIGALI, Uganda, Africa