"I remain a member of the Presidency by the will of those who elected me to this post. I definitely don't want to disappoint them," he told the press in Sarajevo on Wednesday, suggesting that it was the Bosnian Croat people and not himself personally who was exposed to pressure.
He added, however, that he would respect the decision of the international community's High Representative, Paddy Ashdown, if he dismissed him from office.
"My message to representatives of the international community is... if you do decide to replace me, then may it be the last case of such powers being used because this is in the interest of Bosnia's future," said Covic.
He declined to comment on the indictment which charges him with abuse of office and corruption in connection with meat manufacturer Lijanovici. He said this should be done in court.
Covic said the indictment gave a brand new dimension to the Bosnian judiciary because it was issued and confirmed by foreigners and because parts of it appeared in the media before it was handed to the accused.
Covic said he was "shocked by the insinuations and unchecked details" in the indictment, which he added was based solely on the testimony of a protected witness "whose identity is known to everyone".
He labelled the key prosecution witness as a "criminal" whose identity some Bosnian media revealed even though this is punishable.
Covic said that if he lived in a "normal country" he would likely resign without giving it too much thought because it would be the most appropriate and easiest thing to do for himself and his family.
He said the situation in Bosnia was not such and that it would be best for his people and all Bosnian citizens if he stayed in the Presidency. He added his courage stemmed from the Constitutional Court's decision not to fire its president Mate Tadic, who is also accused in the Lijanovici case.
Covic linked the indictment against him with attempts to "remove one people" from Bosnia and "transform it into a national minority".
Addressing Bosnia's citizens, Covic said: "I believe the time has come for us to straighten our backs and preserve Bosnia-Herzegovina for ourselves and our children".