I received a job contract, but the salary is not so suitable. Who should call first: I to them or them to me?

Well, the salary isn’t what I thought. I brought dissatisfaction during the receiving of the contract. However, I said I need time to think about it because I have another contract elsewhere.

Should I call them first or wait. I do hope they will raise their offer to pay for something better, or think how to give a better benefits. If I can them, I think it is like being desperate and it is not true.

They want me to sign the contract right now at place but I said no, I need to read it, think and compare it to another proposal.

What to do next, or just wait and let them think… They know I can get a better offer, but I do like what I’m going to do in that company, but the salary not that good as it should. Any advise?