Healthcare support workers were due to walk out at eight hospitals in the local area from 7am on 10 December until 7pm on 11 December.
Healthcare support workers on band 2 of the NHS Agenda for Change pay scale should only be providing personal care, according to NHS guidance.
However, Unison says healthcare assistants employed by the board have routinely undertaken clinical tasks such as monitoring blood, performing electrocardiogram tests and inserting cannulas. These should be paid at band 3 rates.
The union says it will put the improved offer to the healthcare assistants over the next two weeks to establish whether they want to accept or reject the proposals.
Unison Cymru regional organiser, Lianne Owen, said: ‘It's good to see the board making an improved offer even at this late stage.
‘Nobody wants to go on strike, but it's frustrating that it took the threat of action before board managers were prepared to offer more. The improved deal will now be sent to the staff involved in the dispute to establish what they want to do next.'
Andrew O'Leary, Unison Swansea Bay branch secretary, added: ‘These undervalued staff would much rather be at work caring for patients than on strike. But it is only through them making a stand that this improved offer has been put forward.'