The election was held in course of the ICC annual meeting at Lord's, in order to elect a successor to Walcott whose term expires in July next year.
The nine nations will meet again for a fresh vote in 12 months time.
''We could not achieve a consensus and there was no clear winner in accordance with the rules,'' Walcott said. ''So the members decided that a fresh election would be held during our 1997 conference.''
Dalmiya had the majority of the 22 associate nations, but could only get three votes from the nine Test playing nations. As per rules, the associate nations carry one vote apiece, while the Test nations carry two votes.
Mackerduj and Gray split the remaining six Test votes among themselves in the first ballot, following which the former, who is president of the South African Cricket Board, withdrew from the second ballot.
In the second round of voting, one Test nation abstained, and Dalmiya won over Gray by a margin of 25 to 13. However, the Indian candidate did not get the required two-thirds majority of the nine Test countries, and will have to wait a year before he makes a fresh bid for the honour of being the first Asian head of the ICC.