A Commons committee said replacing the firm Atos – which until March assessed whether people were fit to work – would not address the problems “on its own”.
The report said changes to the system needed to be made “immediately”.
Minister for Disabled People Mark Harper said a new private provider would reduce waiting times.
It comes after the government had criticised Atos – which had conducted Work Capability Assessments (WCA) of claimants – over “significant quality failures”.
The contract with Atos had been due to finish in August 2015, but was ended early. The government has said a replacement was expected to be appointed early next year.
However, the report by the House of Commons Work and Pensions Committee said Atos had become a “lightning rod for all the negativity” around the Employment and Support Allowance (ESA) process.
It said: “Just putting a new private provider in place will not address the problems with ESA and the WCA on its own.”
It found the system was “not achieving its purpose” of helping people move back into employment in the “short to medium term”.
Committee chairman Dame Anne Begg said the current system needed “to be improved now”.
She called for the Department for Works and Pensions (DWP) to “rigorously monitor the service standards to ensure they are being met” and for it to impose penalties if standards were not met, adding: “This has not always happened with the Atos contract.”
Mr Harper, who was appointed as Minister for Disabled People in last week’s cabinet reshuffle, said a new provider would deliver “the best possible service for claimants, increase the number of assessments and reduce waiting times”.
He said more than 700,000 people who had been on incapacity benefit were now “looking for, or making steps to return to work” following a WCA.
“It is crucial that we continue this important process to ensure that people are not written off and we get a fair deal for the taxpayer,” he said.
Several charities have backed calls for fundamental reforms of the disability benefits system.
Richard Hawkes, chief executive of Scope, said “reforms must go deeper than simply changing the provider”.
He said the system needed to ensure disabled people would get the “specialist, tailored and flexible support they need to find and keep a job”.
Steve Ford, chief executive of Parkinson’s UK, added: “This report simply confirms what we have known for years – ESA is a shambolic and hopeless system that cruelly penalises the most vulnerable amongst us.”