"Brahimi should respect his role as a mediator and be fair and neutral," the minister was quoted as saying by the official Syrian Arab News Agency.
Brahimi said Thursday he was concerned presidential elections scheduled in Syria for July could jeopardize any possibility for peace negotiations between members of the opposition and the Syrian government.
He said in a statement that if elections go forward, the Syrian opposition would likely not want to talk with the regime in Damascus.
The Syrian minister said Brahimi is not mandated to weigh in on Syria's political affairs.
"It's not Brahimi's mission to discuss sovereign issues related to the Syrian domestic affair," he said.
The so-called Geneva Communique of 2012 calls for a transitional government to lead Syria to eventual elections.
Brahimi said Thursday he'd "very much" like to move forward with peace processes as the Syrian conflict moves into its fourth year.
"We would like the help of the [Security] Council and of all those who can help to make sure that if, and when, we have the third round, it will be a little bit more productive than the second round," he said.
Two rounds of negotiations were held this year, with few concessions from either side.