The ultimatum issued by Austria-Hungary -- available in full here -- made ten specific demands:

1. Suppress publications which incite hatred and contempt of the Austrian Monarchy, using laws that already criminalized incitement;

2. Dissolve Narodna Odbrana (National Defence) and similar societies agitating for and assisting Serb nationalists in Austria-Hungary, confiscate their means of propaganda, and prevent the societies from reforming under new names;

3. Eliminate from public instruction in Serbia, both as regards the teaching body and the methods of instruction, all that serves or might serve to foment propaganda against Austria-Hungary;

4. Remove from the military service and the administration in general all officers guilty of propaganda against Austria-Hungary, names of which Austria-Hungary reserved the right to provide;

5. Accept the collaboration in Serbia of organs of the Austro-Hungarian government in the suppression of the subversive movement directed against the territorial integrity of the monarchy;

6. Begin a judicial inquiry against the accessories to the plot of June 28th who are on Serbian territory, with organs delegated by the Austro-Hungarian government participating in the investigation;

7. Immediately arrest Major Vojislav Tankosić and Milan Ciganović who were implicated by the preliminary investigation undertaken by Austria-Hungary;

8. Prevent by effective measures the cooperation of Serbian authorities in the illicit traffic in arms and explosives across the frontier and to dismiss and severely punish those in the Serbian Frontiers Service who assisted the authors of the Sarajevo outrage;

9. Furnish Austria-Hungary with explanations regarding statements from high Serbian officials both in Serbia and abroad, who have expressed hostility towards Austria-Hungary; and

10. Notify Austria-Hungary by 5:00 on July 25, 1914 of the execution of these measures

The Serbian response -- while crafted to sound reasonable and only refuse one demand -- essentially rejected demands 1, 5, and 6 since it claimed to have no control over private newspapers (but offered to submit amendments giving it that control to its legislature) and refused to have its sovereignty violated by the presence of Austro-Hungarian personnel on its territory (which it claimed to be "a violation of the constitution and of criminal procedure"). At the same time, Serbia mobilized.

It seems clear enough from the response to the ultimatum that Serbia was unwilling to allow a full-scale investigation that would probably have implicated members of the government. Since (after some initial Russian misgivings) Serbia had a security guarantee from Russia, it could afford to be a little more stubborn than the usual small country facing a contiguous great power. Having said that, the Serbian government seems never to have seriously entertained the demands it ultimately rejected, even before it became clear that it would have Russian military support.

Source: The documents themselves, in their English translations, and

Martel, Gordon. The Month that Changed the World: July 1914. Oxford University Press, 2014.