The 27-year old was sent back to Edinburgh on Friday because of an incident prior to Uganda’s 0-0 draw with Kenya in Kampala on Saturday which left the team sitting second on Group 10 of African Cup of Nations qualifying.
Upon his return to Scotland, Obua told the Scotsman that he has no plans of returning to the national team setup if Mulindwa and Williamson are still involved.
"I don't want to play for this team again. Never, never, never again - unless Mulindwa and Bobby are out of the setup," he said.
"These guys have always wanted me out because I am the most vocal player. But I have given all to this team."
However, ex-Kilmarnock and Hibernian manager Williamson said that the Uganda team had no option but to send Obua home whilst keeping the door ajar for the player to resume national team duties.
"Why would I want David out?" said Williamson. "I never say never but it depends on how David goes about this.
"He made a big mistake on Friday and left us with no option but to ask him to leave.
"David has said he wouldn't work under the president or myself. I don't plan to be leaving any time soon."