Dear,
1. First of all when he was hired, you (the management) would have shown him the salary structure and compensation for the post, right? If he felt that his salary was low, he should have demanded more at the time of interview itself. After accepting the offer and joing the organization and even worked for sometime, then he starts saying that his salary is lower than the market standard, means he is indecisive. Leave alone how important the role is.
2. Secondly, just because someone puts in his resignation, you should not increase his salary. As someone rightly put it, if you start doing so, everyone will start the same strategy of putting you a threat of resigning and then demanding more. There is no end to it.
3. What you should ideally do is that try to understand the salary level of your industry. If you feel that you are paying reasonably a good salary, you need not worry.
4. These kind of people (working only for money) will not look at other benefits such as organization's background, growth opportunities for the organization and self in the long run, conducive work environment, freedom to take decision, etc.
5. Even if you increase his salary, what is the guarantee that he will not still look for a job still. If someone offers a better salary, he will still quit.
6. therefore try to talk to him and have patience till next annual review. If he does not have patience, allow him to push off.
Balaji