He declined to comment on the preliminary results of the ballot, saying he expected political parties to recognise the results as soon as they were released as final.
Petersen told the press there was not much time if Kosovo was to move ahead.
He said it was necessary to hear the voice of the small number of Serbs who did vote as well as the voice of those who did not. He added the fears of the latter referred to the rule of law, the protection of minorities, and decentralisation.
Petersen also said the high turnout at the election was a message to politicians that Kosovo's citizens believed in the road leading to the future.
The chief or the Organisation for Security and Cooperation in Europe Mission in Kosovo, Pascal Fieschi, said the first official results would be released on Monday and the final between October 29 and November 9.
Council of Europe and European Parliament observers said the election was just and democratic.
Expressing satisfaction with how the polls were held, European Parliament delegation chief Doris Pack said this proved that local institutions should be given more powers. She added the European Parliament expected the U.N. Mission in Kosovo to transfer more authority onto the new Kosovo Government.
The chief of the Council of Europe observer mission, Andrey Tehov, said the poor Serb turnout at the ballot was the result of messages from various Serb leaders.