The Government was facing a Tory rebellion by Tory MPs on Monday over calls for a new body to help infected blood victims.
Conservative backbenchers were set to join forces with Labour backing moves to extend interim payouts to more victims of the scandal.
Up to 30,000 people were given contaminated blood products in the 1970s and 80s. Thousands have died.
Culture Secretary Lucy Frazer indicated that ministers are unlikely to shift position, insisting that it was “appropriate” to wait until the ongoing inquiry has concluded.
The Labour party is calling for a new body to be set up to administer compensation.
More than 100 MPs, including Tories Sir Robert Buckland, Sir Edward Leigh and David Davis, are backing the move.
More than 3,000 people died after contracting HIV or hepatitis C after receiving a blood transfusion on the NHS or a treatment made from contaminated blood products.
The amendment was tabled by Dame Diana Johnson, who has campaigned on behalf of victims.
The creation of a compensation body by the end of this year had been recommended by the chairman of the contaminated blood inquiry, Sir Brian Langstaff, a former High Court judge.
“We have made interim compensation awards, there is an inquiry ongoing. That will report next year and that is why we think it is appropriate to wait for the inquiry,” Ms Frazer told BBC Radio 4’s Today programme.
“I can totally understand and this is an absolutely dreadful situation, that is why the Government has already identified compensation on an interim basis and that is why we have got an inquiry”
She said it was “appropriate” to “wait for the outcome”.
“I think it is always appropriate when you put in place mechanisms for review that you await the outcome of those reviews before you make any final decisions,” she said.
An independent inquiry into the scandal was due to publish its final report this autumn but the document will now be published in March 2024 due to the “sheer volume and scale of the material”.
Under an initial scheme, only victims themselves or bereaved partners can receive an interim payment of around £100,000.
In a letter to Chancellor Jeremy Hunt informing him of Labour’s support for the amendment, Ms Reeves described the infected blood scandal as “one of the most appalling tragedies in our country’s recent history”.
She wrote: “This week we have the opportunity to work together to begin to bring justice for the victims.
“Blood infected with Hepatitis C and HIV has stolen life, denied opportunities and harmed livelihoods.”
Labour’s shadow minister for victims and sentencing Kevin Brennan has also tabled an amendment which would require the Government to respond to the final report of the independent Infected Blood Inquiry within 25 days.
“This is not a party political issue,” Ms Reeves said. “All of us have a responsibility to act now to address this historic wrong.
Downing Street said ministers were “prepared to respond as quickly as possible once the final report is published”.
