Voltage, Ampere and and Ohm of a DC motor
The motor will require a startup current which is quite a bit higher than running current, so it's very possible 600mA is not enough (I can't determine the size from the photo - some measurements would be useful so a rough comparison with similar sized motors can be done)
Is there a voltage/current rating plate on the motor? Does it have a model number printed on it? 

What makes you think it is this specific motor? There are many that look exactly the same.  

Anyway, if you really can't find out any more about it, then you will have to do a few tests:

If you have a scope (or multimeter but will be a bit trickier) then measure the voltage across the power supply, then connect the motor. If the voltage sags significantly (e.g. more than a volt or two) then it's quite likely the motor is trying to sink more current than the supply can provide.    

Also, test the winding resistance. Divide the operating voltage by this and you will get an idea of the startup current. It's possible a large capacitor or two across the supply (e.g. let cap charge, then use a series switch to turn motor on) might help it get started if it's not too far off the mark power wise.  

Here is a table of data for a 6VDC motor picked at random:

 

You can see that the starting current is 3.51A, which is about 4 times the max continuous current of 0.84A. If we look at the winding resistance of 1.71&Omega;, we can see that 6V / 1.71 = 3.51A, so this if your peak startup current (before any back EMF develops)   

The measurements for this motor are 22mm diameter and 32mm length. If your motor is a similar size or bigger then it is quite possible it is of a similar or higher power rating and too much for the power supply (although this is obviously far from certain given the widely varying type/quality of motors)