Should I wait for my professor to reply my request for recommendation letter?
Professors are really (really) busy. Most likely he simply did not have time yet to reply to your email. Or maybe he is at a conference and does not have access to the previous two letters on his office computer. He will probably reply to your message later.

To get his recommendation letter quickly the best thing you can do is make it as easy for him as possible. Because you already have two of his letters I suggest you write your own new recommendation letter based on these two, send it to him by email, and ask him to sign it. This is quite common, at least in the different labs in the UK and France where I have worked: many professors ask students to write their own letter, after which they may make a few changes and sign it. This saves them lots of time.

Also, make sure to let him know when your deadline is so he understands the urgency.