The government launched an inquiry on Friday after the U.S. company marking 9 million school exam papers for national tests said results would be at least a week late.
Schools Secretary Ed Balls said the delay was "unacceptable" and would inconvenience schools and headteachers.
Liberal Democrat Education Spokesman David Laws said the marking of the tests had been a "complete and utter shambles."
The national curriculum SATS test results for 1.2 million children in England aged 11 and 14 were due to be delivered to schools next week.
The results for 11 year-olds, taken at the end of their primary school year before they move to secondary schools, will now be published on July 15.
Most of the 14-year-olds' tests will also be delivered on the same date, but some marks, mainly for English, will not arrive till later.
ETS Europe, the educational testing company marking the exams, said it regretted the inconvenience caused by the delay.
The government awarded ETS a 156 million-pound, five-year contract in February 2007 to mark the SATS tests.
An ETS spokesman said the delays had been caused by problems getting exam papers to its 10,000 markers, as well as difficulties with an online system used to submit results.
Balls said "an independent individual of national standing" would chair the inquiry into what had gone wrong.
The government had hoped the introduction of ETS would speed up the delivery of results.
ETS Europe is a subsidiary of its non-profit-making parent, also called ETS, headquartered in Princeton, New Jersey.
