Classical economics says that when demand increases, the supply will decrease (shortage) and the price will increase as people are willing to pay more for items in short supply. But the suppliers' response will be to increase production, so the supply quantity will eventually increase, keeping pressure on the prices to remain level.
So the question could be answered one of two ways, depending on the time frame. I would judge the statement is false, but it isn't written as clearly as I'd like.
suppliers will respond by increasing production