A single-sinker densimeter has been developed for accurate density measurements in the technically and scientifically important regions of the (p, rho, T) surface of fluids (density range 2 kg.m(-3) to 2000 kg.m(-3) temperature range 233 K to 523 K; pressure range 0.2 MPa to 30 MPa). The method used for measuring the density is based on the Archimedes buoyancy principle, but applied in a new way. The buoyancy force exerted by the sample fluid on an immersed sinker is transferred through the wall of the measuring cell by a magnetic suspension coupling to an analytical balance. The new single-sinker densimeter avoids most of the shortcomings of other methods of densimetry, and enlarges the operational range for density measurements in reference quality up to higher temperatures and pressures. In order to test the new apparatus and to determine density values of reference quality, comprehensive (p, rho,T) measurements on pure argon (237 values) and pure nitrogen (177 values) were carried out in the entire working range of the apparatus. The total relative uncertainty of the measurements in density rho was estimated to be <\1.5.10(-4).rho\ to <\2.10(-4).rho\. The experimental results are compared with results of previous studies, and with those calculated from current equations of state. A second paper will report the results of the (p, rho, T) measurements on pure carbon dioxide and pure methane, also carried out with this apparatus.