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The third-largest religious denomination in Canada has rejected allowing its clergy to officiate at same-sex marriages.

At the Anglican Church of Canada's general synod in Vancouver last night, not enough bishops voted in favour of a resolution to change the definition of marriage. It called for deleting the words "the union of man and woman".

The laity voted 80.9 percent in favour, easily passing the required two-thirds threshold. The clergy voted 73.2 percent in favour.

But the bishops failed to reach the requirement of two-thirds in favour, with only 62.2 percent voting yes.

Two bishops abstained, 14 voted against, and 23 voted in favour.

The archbishop of the Diocese of New Westminster, Melissa Skelton, expressed sadness over the result.

She's in hospital due to a recurring medical condition and watched the vote via livestream.

"I was very disappointed not to have been with our delegates on account of my illness as the vote on the marriage canon occurred tonight," Skelton wrote in a message to church members. "All I can say is that I'm very sorry for all the feelings of hurt that this vote has caused, and that I urge everyone to pray for the Anglican Church of Canada.

"Remember that this Synod is not over!" she added. "And so please pray that together we can find a better solution to the marriage question."

The Vancouver Cathedral Anglican dean, Peter Elliott, expressed his sorrow over Twitter.

In 2005, Canada legalized same-sex marriage, becoming the fourth country in the world to do this.

The general synod continues at the Sheraton Wall Centre until Tuesday (July 16).

According to its website, the Anglican Church of Canada has more than 500,000 members in nearly 1,700 parishes.