If your mower starts up, but won't idle or run well, there is a good chance that the carburetor is contaminated with varnish or gum, a brown residue that is left by the gasoline, as you operate the engine, over time. One way to eliminate the varnish would be to add some carb cleaner, gum-out, or fuel injector cleaner, to the 5 gallon gas can that you use to refuel your mower. You can find these items at an auto parts store. If you can get your mower started, and manage to keep it running for 10 or 20 minutes, that will give the gasoline additive a chance to work on the varnish, and after a few weeks, the mower will be back to normal operation. There are other reasons why your mower might not run right. It could be a clogged air cleaner, or some sort of mechanical defect in the throttle. However, the ignition is very likely OK, since it starts up when you prime it and pull the cord...

Has the mower been sitting for a while? Are you saying that it will run only initially for a few seconds? If so, then likely old fuel and/or contaminates in the fuel system and the main jet at least would need to be cleaned. If you are experiencing where it runs, but slow- it is possible the throttle shaft is sticky or some debris is physically holding the linkage.

I have a Toro Super Recycler 2 lawn mower.It starts and runs fine but when I engage the lever for the self propell it barely moves or not at all Thanks for your response

Most likely it's a worn out /// or out-of-adjustment belt.