A union source said that the strikes were planned for Monday, but the employers decided to offer more. He said: "The revised deal will be put back to the sites for the men to decide."
Unions had served employers with notice that steel erectors working on the projects were to begin strike action on Monday.
M&E union Amicus had informed employers that workers intended to strike every Monday and would not work overtime on other days.
Fears are growing at Heathrow that electricians on the site, who are also members of Amicus, may become embroiled in the row.
A BAA spokesperson said: "The national dispute between steel workers employed under NAECI is completely unrelated to the major projects agreement for the M&E sector. "The T5 joint council which comprises Amicus and M&E employers is the custodian of the MPA at T5. It would be their responsibility to advise workers of the implications of any unofficial and unlawful action."
The employers' body the Engineering Construction Industry has said that their pay offer to the steel erectors of an increase of 8% over two years is reasonable. However, as Building went to press, its leaders were in a meeting about the issue and were unavailable to comment. It is understood that they are looking at the validity of the union ballots.