Barclay said that a perception was created that he gives importance to bilateral cricket over 'everything else' but that is far from the truth.
Barclay comfortably defeated Singapore's Imran Khwaja to succeed India's Shashank Manohar in a voting carried out during ICC's annual quarterly meeting.
On July 1 this year, Shashank Manohar stepped down from the post of ICC chairman after twin two-year tenures at the helm.
The process for the election of the next chairperson is expected to be approved by the ICC Board within the next week.
The United States Cricket Hall of Fame recently wrote to Manohar, indicating that they would like to recommend Cameron to the top post of the International Cricket Council.
No Indian contender likely ICC chairman post after Shashank Manohar, chances slim for Sourav Ganguly
Finalising the nomination process to elect the new chairman, T20 World Cup and other administrative matters are on the agenda.
There is some noise about the BCCI fielding a candidate at the election for the ICC chairman post.