Let $R$ be a commutative semiring. The purpose of this note is to investigate the concept of $2$-absorbing (resp., weakly $2$-absorbing) primary ideals generalizing of $2$-absorbing (resp., weakly $2$-absorbing) ideals of semirings. A proper ideal $I$ of $R$ said to be a $2$-absorbing (resp., weakly $2$-absorbing) primary ideal if whenever $a,b,cin R$ such that $abcin I$ (resp., $0
eq abcin I$), then either $abin I$ or $bcin sqrt{I}$ or $acin sqrt{I}$. Moreover, when  $I$ is a $Q$-ideal and $P$ is a $k$-ideal of $R/I$ with $Isubseteq P$, it is shown that  if $P$ is a  $2$-absorbing (resp., weakly $2$-absorbing) primary ideal of $R$, then $P/I$ is a  $2$-absorbing (resp., weakly $2$-absorbing) primary ideal of $R/I$ and it is also proved that if $I$ and $P/I$ are weakly $2$-absorbing primary ideals, then $P$ is a weakly $2$-absorbing primary ideal of $R$.

Keywords: Semirings, Primary ideals, Weakly primary ideals, 2-Absorbing primary ideals, Weakly 2-absorbing primary ideals