This study, using the Microscopic Imager (MI) of NASA Rover Exploration Mission's (REM) ‘Opportunity’, aims to explain the origin of laminated sediments lying at Meridiani Planum of Mars, and of the strange spherules, known as blueberries, about which several hypotheses have been formulated. To this purpose, images of the sedimentary textures of layers and fragments captured by REM have been analysed; sediments that NASA has already established as ‘pertinent to water presence’. Our study shows that such laminated sediments and the spherules they contain could be organosedimentary structures, probably produced by microorganisms. The laminated structures are characterized by a sequence of a thin pair of layers, which have the features of skeletal/agglutinated laminae and whose basic constituents are made by a partition of septa and vacuoles radially arranged around a central one. The growth of these supposed organosedimentary masses is based on the ‘built flexibility’ of such a basal element; it may be a coalescing microfossil formed by progressive film accretion (calcimicrobe), in a variety of geometrical gross forms, such as a repeated couplet sequence of laminae or domal mass and large composite polycentric spherule, both in elevation. The acquired structural and textural data seem to be consistent with the existence of life on Mars and could explain an origin of sediments at Meridiani Planum similar to that of terrestrial stromatolites. The Martian deposits, probably produced by cyanobacterial activity, and the embedded blueberries could represent a recurrent and multiform product of colonies with sheath forms, resembling in shape those of the fossil genus Archaeosphaeroides (stromatolites of Fig Tree, South Africa).