True, when equilibrium price of a good is less than its market price then there will be competition among the sellers. At a price lower than market price, there will be more supply. This is explained with the help of the following diagram.
In the above diagram, point E is the equilibrium point, where the market demand curve DD and the market supply curve SS intersects each other. At this point the equilibrium price is OP and the equilibrium quantity is OQe
Now, suppose the market price is OPo, the equilibrium price is less than the market price. At this price the market demand is OQd and the market supply is OQs. Clearly, market supply is more than the market demand. So, there exists a situation of excess supply. Due to excess supply, there will exist competition among the sellers.