Is it possible to update from 6.0.1 to 6.1.3 instead of 7.0.4? I have iOS 6.0.1 on iPhone 4s. I would like to upgrade to iOS 6.1.3 (afaik latest 6.x for iPhone 4s?) and not to 7.x as software updater suggests.
Is there any way to do so?
In iTunes, on the Summary tab for your device, hold Shift, then click the Update button. This will allow you to manually specify an IPSW file to update your device with.

As for obtaining said IPSW file, there are various links around the web to get the version you want. This article has some links to various IPSW files for various iDevices, as well as additional information on this process.

Note: You cannot downgrade to a prior iOS version using this process.