Running or belt conveyor with electric motors and control panel need a kind of certification to be sold in US market?
The requirement for NRTL listing of electrical equipment is not universally applied; it is actually a State by State addition to the National Electric Code. But the only reasonable way to deal with it from the standpoint of a manufacturer wanting to export to here is to attain an NRTL listing from someone like UL or ETL (Intek) since you don't know where it may end up. You are correct though, CE and other EU approvals mean nothing here.

For something like a conveyor though, you will probably not need other approvals for the machinery itself, unless it is intended to be used in some specific industry that has its own set of regulations. For example mining conveyors often need approval from MSHA (Mine Safety and Health Administration) due to some added safety requirements in case someone falls on the belt.