Balfour Beatty makes agreement to buy two of Mowlem's businesses if Carillion bid succeeds.
Balfour Beatty said on Wednesday afternoon that it was pulling out of the battle with Carillion to buy Mowlem.
However, in a statement to the stock exchange it said that it had "reached a binding agreement" with Carillion that if the latter's recommended £313m, or 220p a share, bid for Mowlem succeeded, Balfour would buy two of Mowlem's businesses - Edgar Allen and Charter.
Edgar Allen is a UK rail track products manufacturer and Charter is a US-based company. Balfour has agreed to pay a total of about £20m to Carillion for the two businesses.
The Takeover Panel had given Balfour Beatty a deadline of today to declare whether or not it would be making a rival for Mowlem, after it initially said it was a possibility on 12 December.
In 2004 Edgar Allen made a £2m profit on a £25m turnover. Charter, which is based in Texas, made a £2m profit on £95m turnover in the same year.