After a two-day Steering Board session, he told reporters in Sarajevo that Bosnian politicians were expected to be more resolute in implementing agreements, including on local elections due in October.
Inzko said that Turkey, a PIC member, had requested that the international community intervene in the holding of elections in Srebrenica so that all prewar inhabitants could vote, but other PIC members declined the proposal.
The PIC also includes the most influential Western countries, Russia and Japan.
Inzko said that he would not use his Bonn powers.
His deputy and Brcko supervisor, Roderick Moore, said the PIC Steering Board supported the suspension but not the termination of international supervision over Brcko District.
Moore said he decided today to suspend his role as supervisor and that his office in the district would be closed on August 31.
He added that he would keep his supervisor powers and that the international arbitral tribunal authorised to decide on the district's final status would continue to operate.
Moore said perhaps the best metaphor was about freezing the supervision and that he had not terminated his supervisor's mandate, adding that all 130 binding orders issued so far remained in force.
He said Turkey was against the suspension of supervision advocated by most PIC members.
International supervision over Brcko in northeastern Bosnia was established in 1999, when an international arbitral tribunal decided, based on an agreement reached during the peace negotiations in Dayton in 1995, that the town should be organised as a territorial and administrative district independent of Bosnia's two entities.
The agreement was reached because the negotiating sides in Dayton could not agree which one should get Brcko, which has strategic significance and now divides the Serb entity in two.
The international supervisor, a US diplomat, had unlimited administrative powers, including the possibility to change any decision made by the local administration.
Moore said Brcko continued to have problems, like the entire Bosnia, such as crime and corruption.
The international community remains committed to helping Brcko, he said, adding that the European Union Delegation in Bosnia would open an office in the district in the period ahead.