In his inauguration speech, Dodik, who was elected Bosnian Serb entity President at the 3 October general elections in Bosnia and Herzegovina, extended apologies for crimes committed during the war in the 1990s against non-Serbs.
"In the next four years, I will be the president of all who have the Serb republic close to their heart, regardless of their political affiliation and ethnicity," Dodik said, adding that the prosperity and the preservation of this entity were his presidential programme.
The vice presidents -- Emil Vlajki as the Croat representative and Enes Suljkanovic,as the Bosniak representative -- were also sworn in at the parliament's special session.
In attendance was Serbia's President Boris Tadic.
Dodik welcomed the latest moves made by Tadic and Croatia's President Ivo Josipovic, saying that they "have ushered in a new optimism in the region".
"We in the Serb republic can give full support to the presidents of Serbia and Croatia who, after two decades, have brought a new optimism which will certainly further stabilise the entire region," Dodik said.
Peace and stability of the entire region are of key interest for the RS, and we will give our full contribution to that, he added.
Dodik said that the RS had earlier apologised for crimes committed by Serbs against other peoples in the last war and on this occasion he also said he was sincerely sorry for "every innocent victim, particularly for victims killed by individuals from the people to whom I belong".
He said that crimes committed against Serbs were very slowly or not at all prosecuted by the courts in Bosnia and Herzegovina.
The entity's president called for terminating the mandate of the Office of the international community's High Representative in Bosnia and Herzegovina and expressed readiness for negotiations with Bosniaks and Croats on future constitutional changes, provided that they did not undermine the current boundaries of his entity.
The entity parliament's speaker is Igor Radojcic.
The new government in the Serb entity will be formed by members of Dodik's SNSD, the Socialist Party in the entity (SP RS) and the Democratic People's Alliance (DNS).