  We report the first direct demonstration of possibility to generate the
extreme ultraviolet (EUV) radiation with a freely expanding jet of dense plasma
with multiply-charged ions supported by high-power microwaves. The detected
emission power is about 20 W at 18--50 nm for argon and xenon and 0.3 W at
13--17 nm for xenon. The discharge with a peak electron density up to $3\times
10^{16}\,$cm$^{-3}$ and a characteristic size of $150\,\mu$m is supported by a
focused radiation of a recently developed gyrotron with unique characteristics,
250~kW output power at 250~GHz, operating in a relatively long (50$\,\mu$s)
pulse mode. Up-scaling of these experimental results gives grounds for
development of a point-like kilowatt-level EUV source for a high-resolution
lithography able to fulfill requirements of the microelectronics industry.
