Open Doors is backing attempts to force the UK Government to take human rights into account in its trade deals with other countries.
It is supporting the 'Genocide Amendment' put forward by Lord Alton to the Government's Trade Bill.
If passed, British courts would have a role in determining whether a country is committing genocide. It would also force the Goverment to review trade agreements with China over its treatment of the Uighur Muslims and suppression in Hong Kong.
Open Doors' head of advocacy, Dr David Landrum, said the Government must "stop turning a blind eye to genocide".
"The deliberate extermination of a whole people group is an extraordinary act of evil," he said.
"If we claim to value goodness and justice, it demands a response."
Passing the amendment would set "a statement of intent for the UK's role in protecting human rights globally", he continued.
"If the amendment passes, it will enable our country to identify genocide and it will compel us to do something about it.
"As things stand, we don't have a mechanism to determine whether genocide is happening and who is complicit in it.
"A high bar will be set for the courts to determine this, and if confirmed it would be for parliament and the government to act."
The UN defines genocide as "acts committed with the intent to destroy, in whole or in part, a national, ethnic, racial or religious group".
However, Open Doors said that trade and global politics have made it "notoriously hard" for the UN to rule that genocide has been committed.
Open Doors is asking supporters to write to their MPs ahead of Tuesday's vote to urge them to support the amendment.
Dr Landrum said that MPs should not be swayed by economic concerns.
"It's clear that the economic impact won't be anything like what it cost the UK economy to abolish slavery," he said.
"Like the abolitionists, we have an opportunity to do the right thing. It's time to stop turning a blind eye to genocide. I hope we pass this moral test."