2001 grand am trouble starting when engine is warm

I have a 2001 grand am SE with 69k miles. Here's the problem: I go out in the morning and my car will start right up, but if I drive somewhere and come back to my car about a half hour or even up to 3 hours after it was running last and start my car it will crank for a few seconds and sound like it is starting but when u stop turning the key it will not be started, you have to hold the key for a few more seconds and then it will start, but even then it seems like the car doesn't want to start. Here's the confusing part: if you press the gas pedal a little bit the car will start up without any problems. It only has the starting problem when the engine has been recently running or hasn't cooled down completey. Please help with this!

What engine?

Pull the vacuum hose off of the pressure regulator turn the key on and off a couple of times. If gas comes out replace it.

3.4L V6 175hp