Ashdown appointed Vinko Dumancic DGS chief as a representative of the Croat people, while Vahid Alagic was appointed his deputy as a representative of the Bosniak people.
Ashdown also appointed three department heads in the State Agency for Investigations and Protection (SIPA).
Ashdown's office in Sarajevo said in a statement that the High Representative regretted having to make the decision considering that the DGS had been without a director since February last year.
The appointment of top DGS officials was discussed by the Council of Ministers on Thursday, but the discussion ended without the necessary agreement.
Prime Minister Adnan Terzic told reporters he had to vote against the nominated candidates, particularly against Robert Peric, although he was the best candidate for the post.
Terzic said his party, the Party of Democratic Action (SDA), believed that by appointing a Croat as DGS director would disrupt the ethnic balance in law enforcement institutions.
He said the situation was caused by Foreign Minister Mladen Ivanic who previously refused to support a Croat candidate for the post of SIPA chief, after which Ashdown appointed to the post Sredoje Novic, a Serb.
Terzic claims that Ivanic breached the agreement between the parties concerning the distribution of important posts in state agencies, which now continues to generate new problems.
Ivanic in turn accused Terzic of causing a new crisis in the country by refusing to vote for the new DGS chief and of putting party interests before national interests.
After the problems with the appointment of SIPA chief Terzic relieved Ivanic of his duties, which led to an impasse, with Ivanic refusing to step down and Terzic lacking instruments to dismiss him.