A Christian couple in the US have closed their bakery store after a feud with gay rights advocates over their refusal to make a wedding cake for a lesbian couple. 

Sweet Cakes by Melissa was contacted by Rachel Cryer and Laurel Bowman who asked for a tiered wedding cake.  

When Sweet Cakes owners Melissa and Aaron Klein refused on grounds of their religious beliefs, Cryer and Bowman complained to the authorities.

The Kleins say they have since received hate mail and claim that their customers were "badgered and harassed" into no longer doing business with the bakery, based in Gresham, Oregon.

According to The Blaze, one of the emails sent to the couple read: "You stupid bible-thumping, hypocritical b**ch.  I hope your kids get really, really sick and you go out of business."

Another said: "Here's hoping you go out of business, you bigot.  Enjoy hell." 

The Blaze report said that some existing orders with the bakery were cancelled as a result of the dispute.  

On Friday, the bakers posted a message on their Facebook announcing the closure of the store: "This will be our last weekend at the shop we are moving our business to an in home bakery." 

Mr Klein said that at the time of the order, he had apologised to Bowman and Cryer "for wasting their time and said we don't do same-sex marriages".

The lesbian couple claim that Mr Klein described them as "abominations" but he denies this.

"[I] honestly did not mean to hurt anybody, didn't mean to make anybody upset, [it's] just something I believe in very strongly," he said.  

He told NBC that he and his wife should be free to serve whomever they want according to their beliefs.

"I'm free to exercise my religion however I see fit. I should not be compelled to violate my conscience," he said. "If I'm told I have to make a wedding cake for a same-sex marriage, I feel that I'm violating my beliefs. I don't think I should have to do that."

The Kleins have not held back from making their religious beliefs known through their company. On the Sweet Cakes website, the couple say they "strongly believe that when a man and woman come together to be joined as one, it is truly one of the most special days of their lives".

They also quote John 3:16: "For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life."

NBC footage of the store showed a Bible displayed on the shop counter and decorative crosses hanging on the wall.

Although business has reportedly suffered because of the row, a note posted on the door of the bakery on Sunday reportedly read: "This fight is not over. We will continue to stand strong. Your Religious Freedom is becoming not Free anymore. This is ridiculous that we cannot practice our faith. The LORD is good and we will continue to serve Him with all our heart."

Oregon's state Bureau of Labor and Industries is currently investigating whether the Kleins violated the Oregon Equality Act of 2007, which states that people cannot be denied a service on the basis of their sexual orientation.