Let \(R\) be commutative ring. As defined by the authors, an ideal \(Q\) of \(R\) is a uniformly \(2\)-absorbing primary ideal if there exists a positive integer \(n\) such that whenever \(a,b,c \in R\) satisfy \(abc\in Q, ab\notin Q\) and \(ac\notin \sqrt Q\), then \((bc)^{n}\in Q\). The authors also introduce and study special \(2\)-absorbing primary ideals (the case \(n=1\) in the preceding definition). Among many other results, the authors prove, for example, that the intersection of two uniformly primary ideals of \(R\) is a uniformly \(2\)-absorbing primary ideal.