Stellar models applied to large stellar surveys of the Milky Way need to be properly tested against a sample of stars with highly reliable fundamental stellar parameters. We have established a program aiming to deliver such a sample of stars. Here we present new fundamental stellar parameters of nine dwarf stars that will be used as benchmark stars for large stellar surveys. One of these stars is the solar-twin 18Sco, which is also one of the Gaia-ESO benchmarks. The goal is to reach a precision of 1% in effective temperatures (Teff). This precision is important for accurate determinations of the full set of fundamental parameters and abundances of stars observed by the surveys. We observed HD131156 (xi Boo), HD146233 (18 Sco), HD152391, HD173701, HD185395 (theta Cyg), HD186408 (16 Cyg A), HD186427 (16 Cyg B), HD190360 and HD207978 (15 Peg) using the high angular resolution optical interferometric instrument PAVO at the CHARA Array. We derived limb-darkening corrections from 3D model atmospheres and determined Teff directly from the Stefan-Boltzmann relation, with an iterative procedure to interpolate over tables of bolometric corrections. Surface gravities were estimated from comparisons to Dartmouth stellar evolution model tracks. We collected spectroscopic observations from the ELODIE spectrograph and estimated metallicities ([Fe/H]) from a 1D non-local thermodynamic equilibrium (NLTE) abundance analyses of unblended lines of neutral and singly ionized iron. For eight of the nine stars we measure the Teff less than 1%, and for one star better than 2%. We determined the median uncertainties in log g and [Fe/H] as 0.015dex and 0.05dex, respectively. This study presents updated fundamental stellar parameters of nine dwarf stars that can be used as new set of benchmarks. All fundamental stellar parameters were based on consistently combining interferometric observations, 3D limb-darkening modelling and spectroscopic analysis. The next paper in this series will extend our sample to giants in the metal-rich range.