Is part of an output of secure PRNG also cryptographically secure? Lets say I generate 192 bits using some secure PRNG. If I now take first 128 bits is it equivalent of generating 128 bits in the first place?

P.S. More practical application for me is that I need a machineKey for the ASP.NET, I use IIS UI for it and it generates a string that corresponds to 192 bit key used for AES, but since AES 128 is good enough as well, but faster, I want to take only the first 128 bits.
Yes. Although the bit values are not identical per se (even given the same seed) you should use any of the 192 bits to form a 128 bit key - as long as you don't reuse any bits of course.

If the 128 bits are not secure, then the 192 bits should also not be secure. AES keys consist of bits that are entirely random and thus unrelated, so generating a 192 bit key and then using the leftmost 128 bits should be OK.