But if they are found to be the father of the child they will have to pay back the cost of the test - estimated at up to pounds 400.
Ann Chant, head of the agency, giving evidence to the Social Security Select Committee, told MPs: "The further use of DNA tests could be something of a breakthrough in this area ... We now can say (to the man) have a DNA test and we can pay for it."
But Miss Chant said that in the 440 cases of paternity that reached court this year, 94 per cent of the men involved were judged to be the father.
She also told MPs that the Child Support Agency savedpounds 479m in benefits last year, pounds 19m more than had been forecast, and has already "paid for itself". She said over 60,000 parents had come off income support after they received a maintenance application form, which accounted for pounds 199m. The year previously pounds 138m had been saved.
In all more than pounds 1bn had been saved from 1993-94 to August 1995, and Miss Chant said that the CSA's running costs since it was started up three years ago had been pounds 500m.
In July the CSA's position was described as "financial chaos"by Labour's social security spokesman, Donald Dewar, after it was revealed that the debt from absent parents had reached pounds 525.5m, money that was unlikely ever to be collected.
New figures showed that by the end of August the total amount of maintenance assessed but not paid had risen to pounds 701.9m.
Miss Chant said: "This is a large sum but the rate of interest has reduced in recent months, which reflects the action the agency is taking to reduce the amount of doubtful debt charged."
There were several reasons for so many parents coming off income support, such as reconciliation or the parent who looks after the child finding an alternative source of income, such as a job. "But when a very large number of couples go off the books straight away it is impossible not to think of collusion," she said.
She also said the CSA was working closely with the Benefits Agency to investigate allegations of fraud or evasion made by one parents against another. Of 7,610 cases sent to the Benefits Agency in the nine months to last November, 39 per cent "had identified a fraudulent element".
"For good or ill the agency has become a lightning conductor for those wanting to report [alleged fraud]," she said.Reuse content