The National Union of Teachers is asking its members carry out the tests after ministers promised to commission new studies on how the tests are working and consult teachers on the findings.
The union's members will be balloted next month, but will be told they can still refuse to carry out the tests if they mean an unreasonable workload.
The NUT, the last of the three main teaching unions to continue its boycott, was finding its position increasingly untenable. While it had argued that the tests were educationally unsound its action had to be based on workload issues to be legal, and these had largely been resolved.
The National Association of Schoolmasters Union of Women Teachers and the Association of Teachers and Lecturers called off their action after concessions on testing and the slimming down of the national curriculum.
Doug McAvoy, the NUT's general secretary, who has been looking for a way out of the dispute, met the Secretary of State for Education, Gillian Shephard, last Thursday and was offered a face-saving solution. The Government will allow teachers to give their views on its evaluation of the tests.
While ministers are unlikely to change their conviction that written tests are the best method of assessing children's and schools' performances, they may make some concessions to teachers' views. For example, the unpopular Shakespeare tests could be dropped.
Mr McAvoy hoped the Government's study would strengthen the union's campaign.
"For the first time there will be an evaluation of the professional and educational issues, whereas previously only workload was being considered by the Government. By co-operating it will be possible for us to bring detailed examples which will support the statements we have been making," he said.
Mrs Shephard was cautious about the evaluation."I have taken a series of steps to respond to teachers' concerns about workload and to enhance teachers' professionalism. I am glad that the NUT executive has responded in a professional and considered way."