K-shell emission from copper target was observed by focusing femtosecond laser pulses very close to the target surface-air interface. It was shown that mechanism of X-ray emission is connected with generation of fast electrons in the air plasma area. Experiments demonstrated that moderate intensity of laser radiation (IL < 1015 W/cm2) was enough to produce considerable flux of X-ray photons of at least 10 keV energy. The parameters of generated X-ray emission were studied. It was found that after propagation through 40 cm thick air layer X-ray spectra consisted of pronounced Kα and Kβ characteristic lines and relatively small Bremsstrahlung continuum. Since transversal source size has an order of a few tens of micrometers, such a source can be used for absorption imaging of micro-objects in standard laboratory conditions. That can be particularly important for diagnostic of medical and biological samples in vivo.