Carillion’s decision came as Balfour rejected a third approach on Wednesday morning.
Balfour also said it would not be asking for an extension to Thursday’s takeover panel deadline.
Carillion confirmed in a Stock Exchange announcement: “The Board of Balfour Beatty has not agreed to Carillion’s proposal or to request an extension to the Put Up or Shut Up deadline which expires at 5pm 21 August 2014.
“Carillion therefore today announces that it is no longer pursuing such a merger.”
The move means Carillion cannot come back with another offer for Balfour for at least six months.