. @xld2s59 we are not working on a 6.1.3 jailbreak, that would be too much efforts for a minimal update. We're waiting for a major release.Understand that the team Evad3rs is not working on a jailbreak for iOS 6.1.3 witch would be a waste of time and energy for them , in short they expect a new update more important.
— pod2g (@pod2g) April 2, 2013
Right now, iOS 6.1.3 cannot be jailbroken untethered with evasi0n. On the other hand, those with an iPhone 4, iPod touch 4G, or iPhone 3GS can still jailbreak tethered on iOS 6.1.3 with redsn0w (untethered for iPhone 3GS if it has the old bootrom). It is expected that Apple may release additional minor software updates before we see iOS 7, which also probably will not be jailbroken untethered.
These minor software updates are expected to only continue to improve iOS security, especially since the software update (iOS 6.1.3), which was designed to fix a lock screen security issue on top of other security fixes, introduced yet another lock screen security issue that Apple will likely want to fix in the future with yet another software update.
If you are jailbroken right now and you’re happy with it, we recommend that you just sit tight where you are and enjoy the large library of tweaks, themes, and applications that Cydia has to offer. There is no reason to update to iOS 6.1.3 if you haven’t already. Those already on iOS 6.1.3 will just have to be patient, and wait for the next major release of iOS to be jailbroken.