Ministers oppose the plans and have offered rebel MPs a so-called compromise, which would boost the ability of parliamentary select committees to consider genocide allegations.
But MPs leading the rebellion have rejected the government's alternative as "meaningless", saying select committees can already look at genocide claims and their rulings can be ignored by ministers.
The parliamentary battle will come to a head on Tuesday during a vote on the Trade Bill.
Last week, peers in the House of Lords heavily defeated the government and inserted an amendment - proposed by Lord Alton - giving the High Court the right to hear genocide cases.
Normally genocide allegations are heard only by international courts, but campaigners say this happens rarely because cases are often vetoed in the United Nations' security council.
They want British courts to hear genocide cases so that persecuted minorities, such as the Uighurs in Xinjiang, China, can have their situation considered by a court of law.
A legal opinion by senior barristers at Essex Court Chambers has already concluded there was a "very credible case" that the Chinese government was committing genocide against the Uighurs.
'Specific duty to act'
The government has now put its name to an amendment originally proposed by Tory MP Sir Bob Neill - the chairman of the Justice Select Committee - which would give a greater role for select committees to consider genocide cases.
The prime minister's official spokesman said the government shared people's grave concerns about human rights abuses in Xinjiang.
"However, [the rebel] amendment could embroil the courts in the formulation of trade policy and conduct of international relations and risks undermining the separation of powers," he said.
"The amendment put forward by the chair of the select committee, which the government will be supporting, addresses the concerns raised by the parliamentarians to take a stand on credible reports of genocide by a prospective trade partner while ensuring a specific duty on government to act."
But on Monday, 355 Uighur survivors wrote to Sir Bob, urging him to abandon his amendment.
They wrote: "Mr Neill, we beg you. Withdraw your amendment. Please allow our people the opportunity to receive justice."
Nusrat Ghani, the Conservative MP who is helping to organise the rebellion, said the government's compromise was "meaningless".
She said select committees could already prepare reports on genocide, but there was no obligation on the government to act.
Ms Ghani added: "As the government has said repeatedly, the only time they will accept, use and recognise the term genocide is when it has been discussed, debated and evaluated and come to a determination in a judicial setting.
"Without the courts, the UK government - just as it has always done over the last 75 years - will not accept the term genocide, so we need a court process engaged in this."
'Used as a fig leaf'
Lord Alton also said MPs and peers who would be involved in making the government's compromise work were opposed it.
"Both select committees have said they would not wish to take on this role without having the opportunity to then refer the issue to the High Court," he said.
"If the government were serious about the compromise, they would incorporate it within this proposal."
Lord Alton said MPs and peers were not impartial like a judge and would not have the time to consider genocide cases.
He added: "I am not surprised that members of the Foreign Affairs Committee have been so outspoken in saying they would not be used as a fig leaf."
The former Conservative leader, Sir Iain Duncan Smith, has tabled a new amendment, which would allow MPs or peers to refer genocide cases to the courts.
"The government has constantly stated that only a court can decide on genocide and call it genocide and yet they are blocking any access to the UK court," he said.
"The Foreign Office particularly doesn't want to do this because they are worried it will upset the Chinese."
The SNP's leader at Westminster, Ian Blackford, said the government's compromise was a "wrecking amendment".
He added: "It is about trying to create that distraction from what we should be doing which is passing the amendment that has come from the Lords.
"I would ask all parliamentarians not to be seduced by what is a distraction and wrecking amendment."