IT company Atos has confirmed it is seeking to end its government contract to assess whether benefits claimants are fit to work.
Staff carrying out work capability assessments for Atos have received death threats online and in person, according to the Financial Times.
In a statement, Atos pledged to carry on undertaking the tests until a new company was in a position to take over.
But the government said that standards at Atos had declined unacceptably.
Disability campaigners have described the work tests as "ridiculously harsh and extremely unfair".
The Financial Times reported that Atos recorded about 163 incidents of abuse or assault on staff each month last year.
It said it had found comments on social media accusing staff of being "murdering scumbags" who "won't be smiling when we come to hang you".
Atos said: "For several months now, we have been endeavouring to agree an early exit from the work capability assessment contract, which is due to expire in August 2015.
"Despite these ongoing discussions, we will not walk away from a front-line service. Our total focus remains on delivering the services we are contracted to provide in a professional and compassionate way until a new service begins."
BBC political correspondent Iain Watson said the government was furious with Atos for leaking information it believes to be commercially confidential.
"In other words, if Atos wants to pull out early some other companies may pay less to take those contracts on than they otherwise would," he said.
The Department for Work and Pensions (DWP) said: "Atos were appointed the sole provider for delivering work capability assessments by the previous government.
"In July we announced Atos had been instructed to enact a quality improvement plan to remedy the unacceptable reduction in quality identified in the written reports provided to the department.
"We also announced in the summer we will be bringing in additional provision to deliver work capability assessments with the aim of increasing delivery capacity and reducing waiting times.
"The invitation to tender will set out that the quality of assessments and service delivery is central to how work capability assessments are delivered."
Labour's shadow minister for disabled people, Kate Green, said: "People have been badly let down by Atos which is why Labour has called on the government to sack them with immediate effect.
"But changing the contract isn't enough. It's time for the government to fundamentally reform Work Capability Assessments so that disabled people who can work are given support they need to find a job."
Work capability assessments were introduced in 2008 to determine who should receive employment and support allowance although Atos' involvement in government benefit contracts dates back to 1998.
Decisions are taken by officials at the DWP using evidence from the assessments, carried out by the French company's Atos Healthcare subsidiary.
In 2012, the National Audit Office said the DWP had failed to penalise Atos for "underperformance", and had not set "sufficiently challenging" targets.
But ministers have said that nearly a million people who applied for sickness benefit have been found fit for work.