The government has pushed back the deadline for schools to submit writing assessments for 11-year-olds, after bringing the date forward a month ago.
Teachers' unions in England had complained that the timescale would not give schools enough time to prepare.
"It will take time for teachers to understand the detail," said schools minister Nick Gibb in a letter to the National Association of Head Teachers.
Labour said the changes were causing "chaos" in schools.
Since the mid 1990s, the tests, often known as sats, have been taken by primary pupils in England to assess their ability in English and maths.
Until the latest change, this year's deadline for schools to submit assessments by teachers of their pupils' writing tests, would have been four weeks earlier than last year.
Schools were worried the shorter timescale would raise pressure on both staff and pupils as it coincided with higher standards demanded in the tests.
In the letter, Mr Gibb told the NAHT's general secretary Russell Hobby that he was "prepared, for this year only, to relax the deadlines in recognition of the unique circumstance of teachers working with a new framework to new standards".
Mr Gibb said teachers would now have until the end of June to submit the data.
He also pushed back to the same date the deadline for submitting data for tests on seven-year-olds.
In the letter Mr Gibb said he remained "committed to the high standards that we have set for the primary phase".
The pair met last week to discuss the concerns of head teachers about the changes.
Commenting on the decision, Mr Gibb said the government had worked closely with teachers and head teachers "throughout this important reform process" and continued to listen their concerns.
"We are working constructively with the teaching profession and their representatives to find solutions to some of the remaining issues," he said.
"The NAHT's readiness to work with us, rather than use the media to scaremonger, has meant that we have been able to have a sensible discussion.
"As a result we have made changes, which I hope will allay teachers' concerns about workload and disruption," the minister added.
Mr Hobby said the dialogue had led to "some productive developments", adding that there were "still areas of doubt to resolve and a bigger picture on primary assessment generally about which we are very concerned."
The National Union of Teachers says "confusion still reigns" and wants this year's tests suspended.
"Nick Gibb's announcement does something, though not nearly enough, to address the chaos. The plan remains in place, and will do damage to the learning of many children," said NUT general secretary Christine Blower.
Labour's shadow schools minister, Nic Dakin, said the deadline change was "yet more evidence of the chaos the Tories are causing in schools and our children's education."
"This Tory government's piecemeal approach to assessments lacks any joined-up or coherent strategy, and is creating confusion for parents and pupils year on year.
"Parents deserve to know exactly how their child is performing at school - but under the Tories, this constant chop and change is threatening standards, causing confusion, undermining confidence in results, and adding extra bureaucracy for teachers," said Mr Dakin.