Adsorption of silicon and carbon atoms at polar SiC(0001) and SiC(0001) surfaces at low coverage was studied using ab initio calculations. The single Si atom is adsorbed in the H3 site at both surfaces, saturating broken bonds of the three neighboring atoms. The adsorption of carbon atom at carbon terminated SiC(0001) surface leads to sp(2) graphene-like reconstruction and the release of silicon atom. The adsorption energy of all constituents is high, exceeding 6 eV. The energy barriers for diffusion of all atoms were calculated showing that Si atom is highly mobile at SiC(0001) surface. C adatom at SiC(0001) and Si adatom at SiC(0001) mobility is several order of magnitude lower. C adatom destroys SiC(0001) lattice, thus excess of carbon is detrimental to SiC growth.