Is 'its' a possessive pronoun?

I know ‘its’ is a possessive adjective. e.g. The dog is wagging its tail.
But is ‘its’ a possessive pronoun? Some books say yes but some say no, some even don’t mention it.

It can serve that purpose, yes: My clock and I both have faces, but I can wash mine while it cannot wash its.

Dear Sir
For posssessive Pronoun, I have given one example like you, please tell me whether
it is correct or not?

My table and I both have legs, but I can move myself while it can not move itself.

Hi Shanthisethuraman,

In your example ‘itself’ is a reflexive pronoun. Your sentence is correct but we usually write ‘cannot’ as one word

Ala

Dear Alan Sir
Thank you for your kind reply, we also used write (cannot) one word
while typing I made mistake. Thank you once again.

S.Shanthi