The BBC reported that transitional arrangements between the UK and Scottish governments for this to happen had been extended, quoting a letter from work and pensions secretary Mel Stride.
Social security powers were devolved to the Scottish Parliament in 2016 following the 2014 independence referendum and amounts to £2.8 billion of expenditure.
The letter, sent to social justice secretary Shona Robison, warned there should be “no further slippage” in the agreed timetable for transferring who delivers the benefits.
Mr Stride wrote: "Any changes to this plan, including unexpected delays or the introduction of additional requirements or benefits into the timetable, would create significant delivery risks.”
The benefits which will continue to be administered by the UK Government include the disability living allowance.
Ben Macpherson, Scottish government minister for social security, announced the Carer Support Payment would be introduced by the Scottish Government in the coming year – the 14th since the Social Security (Scotland) Act was approved by MSPs.
He said: “Introducing 14 new payments in just over five years is no mean feat. We have built this social security system from scratch, working with the people who will use it to make sure that we provide an improved experience and one that treats people with dignity, fairness and respect.
“Our delivery progressed despite a global pandemic. This was recognised by Audit Scotland who commended us for continuing to successfully deliver new and complex social security benefits in challenging circumstances.”
The delays to the handover of social security has taken significantly longer than first anticipated, with set-up costs for the government agency Social Security Scotland now sitting at around £685 million.
Covid-19 has also impacted the process, with the initial target of 2020 dropped due to the pandemic.
Scottish Labour MSP Pam Duncan-Glancy said: "Every day that this programme is delayed is another day that disabled people and carers are left at the mercy of a Tory-run DWP [Department for Work and Pensions].” Scottish Conservative MSP Miles Briggs added: "Promises made by SNP ministers around the establishment capabilities of Social Security Scotland have come and gone."
A Scottish Government spokesperson said: "This is and has always been a joint programme of delivery between both governments.”