The support services firm also revealed it has been in talks with Balfour's major shareholders after two proposals to the company's board were rejected.
It has sweetened its offer by promising to pay an additional 8.5p a share dividend to Balfour investors and told them the creation of a new FTSE 100 company will result in £175 million a year in cost savings by 2016.
Carillion will also refocus Balfour's troubled UK construction services business on a smaller number of contracts so that two-thirds of group profits will come from services and investments with one third from construction.
The company said: "Carillion continues to believe in the powerful strategic logic and financial benefits of a merger with Balfour Beatty and is therefore continuing to consider its position."
Carillion also issued half-year results in which it said pre-tax profits rose by 5% to £67.5 million, helped by progress in rescaling its own UK construction arm.
Balfour revealed on Monday that executive chairman Steve Marshall met Carillion counterpart Philip Green for talks a week ago following the rejection of an earlier proposal.
But the potential tie-up continues to founder on Carillion's wish to cancel Balfour's planned £200 million sale of its US business Parsons Brinckerhoff.
Balfour said its current plan to refocus and simplify the group "remains the most attractive option". However, half-year results this week showed underlying pre-tax profits fell by 53% to £22 million, while losses in construction services widened to £69 million due to previously reported UK issues.
Carillion said today that the £175 million a year of savings will come from back and head office functions as well as from applying Carillion's business operating model to Balfour Beatty's UK business.
It disclosed the content of its meetings with Balfour shareholders following a request from the UK Takeover Panel.
Shares in Carillion and Balfour Beatty were both higher today.