How to negotiate a higher, fairer contact rate?

Hi there,

I am new to the contracting world in the last few months and accepted a 6 month contract at a reasonable, but low rate for 6 months based on my experience, qualifications, and other soft skills.

Similar position contractors are the same company are on a higher rate with lower experience and no official qualifications.

Naturally I feel I am being paid lower than the market rate, and am being offered rates far higher elsewhere.

My contract is due for negotiations in 1.5 months, what should I do?

I like the company however I feel I am not being paid fairly and am prepared to walk away from re-negotiations if they cannot offer my expectations.

Please can anyone experienced in this advice.

Edit: My situation is I am contracting through an agency to a consultancy company who is working for a client.