The Kansas senator had previously said he would consider ending his campaign for the GOP nomination if he could not finish in the top four.
Brownback made the comments while fielding questions in a live Internet discussion on washingtonpost.com.
In response to a questioner who asked whether Brownback planned to end his bid if he places outside the top four contenders, Brownback said, "That is correct. I need to finish in that group to move on forward."
A poll conducted for The Des Moines Register earlier this month shows Brownback in seventh place and drawing support from just 2 percent of Republicans surveyed.
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