Balfour revealed that executive chairman Steve Marshall had met Carillion chairman Philip Green for talks a week ago following the rejection of an earlier proposal.
But the potential £3 billion tie-up continued to founder on Carillion's wish to cancel Balfour's planned £200 million sale of its US business Parsons Brinckerhoff.
Balfour insisted that the sale was a "key strategic objective" and concluded that the merger was not in the best interest of shareholders, despite Carillion's revised offer to pay for bidder costs and allow Balfour shareholders to receive a 2014 dividend.
Mr Marshall said: "Those adjustments were not significant in the context of the overall transaction and didn't mitigate the concerns that the board had - but we thought very hard before coming to our conclusion.
"The board's conclusion is very clearly set out and the rejection therefore is firm."
Balfour said its current plan to refocus and simplify the group "remains the most attractive option" though it would still weigh up "strategic value creating opportunities across the group". The deadline for the offer expires on August 21.
Meanwhile, Balfour brought forward interim results for the half-year to June 27, which showed underlying pre-tax profits falling by 53% to £22 million.
It said the results were in line with its latest trading update when it warned of a shortfall in its UK construction arm.
The company is still looking for a new chief executive after the departure of Andrew McNaughton earlier this year in the wake of a profits warning.
Mr Marshall declined to comment when asked if he was under pressure from investors to press ahead on talks with Carillion.
But he insisted Balfour was confident in its plans, as the UK's biggest construction group, to continue as a stand-alone company, pointing to its £13 billion order book.
However, Mr Marshall admitted the first half had been "disappointing".
Operating losses for construction services widened to £69 million from £39 million in the same period last year, dragged down by the UK.
Balfour said it had seen an improvement in the quality of new orders, with joint venture awards such as a £160 million Sellafield nuclear facility contract and a £184 million "smart motorway" upgrade for the M60 and M62.
Margins on new bids were improving but would "take time to feed through into profitability", the company said.
Balfour added that, as previously warned, its major projects saw further cost increases of £10 million and delays during the first half. Its Cheadle-based engineering services business saw an "extremely challenging six months".
The total size of the company order book combined with orders awarded but not yet contracted was up 26% year-on-year, it said. But these long-term projects would not benefit financial performance until 2016.
Balfour has previously said it is on a 12-18 month programme to revive its construction business.
Carillion said: "The board of Carillion notes this morning's announcement by Balfour Beatty.
"The board of Carillion will give further consideration to its position and will make a further announcement in due course. In the meantime, there can be no certainty that any offer will be made by Carillion or as to the terms on which any such offer might be made."