High-power microwave sources have been widely applied for material processing in scientific research and manufacturing. The development of stable, high-frequency, high-power microwave sources is essential for achieving efficient microwave processing. This study proposes using a square doubly reentrant coupled-cavity as the slow-wave resonant structure in a K-band extended interaction oscillator (EIO). This design allows for ease of fabrication and high-power capability. The EIO is designed to operate in single 0-mode. The simulation results show that the competing π/5-mode can be effectively suppressed by properly choosing the width and location of the output coupler. The simulation and experiments successfully demonstrate stable, single-mode, tunable, high-performance operation of the EIO. The experimental measurements show a maximum output power of 1.776 kW (18.56% electronic efficiency), and a wave frequency of 24.324 GHz at a beam voltage of 17.4 kV and beam current of 550 mA. The EIO microwave source is suitable for interdisciplinary applications that require higher heating rates and greater uniformity.