Weathering of olivine basalt by H2SO4-HCl aqueous solutions at the conditions of early Mars was investigated through numerical modeling in a system open with respect to CO2 and O2 only. The model includes dissolution rates of primary and secondary minerals and oxidation rate of aqueous Fe2+, as well as chemical equilibration among solutes, dissolved gases, and precipitates. The results reveal fast dissolution of Fe-Mg minerals at low pH, followed by preferential dissolution of plagioclase at higher pH. Correspondingly, solutions evolve from acidic, Mg-Ca-Fe2+-Fe3+-Al3+ compositions toward Na-rich alkaline fluids. The period over which neutralization and mineral precipitation may occur is shorter at higher initial pH, lower water to rock ratios, and larger mineral surface areas. Early stages of weathering are characterized by the formation of amorphous silica, goethite, and kaolinite, while zeolites and carbonates form considerably later at higher pH, where silica dissolves. Slow oxidation of Fe2+ causes precipitation of ferrous phyllosilicates. Comparison with Martian observations indicate that amorphous silica, Fe3+ oxyhydroxides, and Mg-, Ca-, and Fe-sulfates could have formed during multiple short-term episodes of acid weathering that were terminated by freezing and/or evaporation. Throughout history, impact generation of oxidants (e.g., O2, SO3, NO2) caused formation of strong acids and incremental Fe2+ oxidation, the processes that are not efficient during O2-deficient periods of volcanic degassing. Although impact-generated acid rainfalls could have caused intense weathering and erosion in Noachian time, dilution of acids and a prolonged existence of surface solutions favored local neutralization of solution, and formation, transport and deposition of clays.