How can a recent graduate effectively negotiate their salary?

I’m a recent graduate and have been contacted about an opportunity at a service-based company. After an interview, they expressed interest in moving forward with my application. When asked about my expected salary, I quoted the average amount that graduates from my department typically receive during campus placements. However, the HR representative mentioned that the client believes my expectation is beyond their budget and provided a very limited salary range.

The position would involve working with a well-known client with a strong reputation, but it requires relocating to a part of the country that I’m not particularly keen on. I’ve communicated my reluctance to the HR, who suggested that a relocation could be possible later on if my manager agrees. I’m skeptical about that possibility.

I’m open to relocating for a better compensation package, but I’m also aware of the challenges in the current job market. I’m uncertain if pushing for my expected salary is the right move at this point. Should I attempt to negotiate further? If I do, how can I approach this effectively as a newcomer to the workforce? Alternatively, should I consider just accepting the offer within the client’s budget?