The increase in intraday electricity market volumes due to intermittent renewable generation may give a strategic producer an opportunity to exert market power. We study offering strategies of a flexible producer in day-ahead and intraday markets using a bi-level model in which the upper level represents the profit-maximization problem of the producer and the lower-level problems clear the day-ahead and intraday markets sequentially. Using a three-node network, we first demonstrate that a flexible producer with perfect forecasts can increase its profit in both markets by coordinating its offer so as to cause transmission grid congestion or lack of competitive generation capacity. Moreover, we show that strategic behavior is possible even when the day-ahead and intraday markets are cleared simultaneously to lower balancing costs. We next assess these market designs in a Nordic test network and offer an explanation for high Nordic intraday prices. Finally, via an annual simulation using the Nordic market data, we verify that strategic offering in day-ahead and intraday markets under imperfect forecasts leads to increased profits vis-a-vis perfect competition but are mitigated through simultaneous market clearing.