Current restrictions on the use of antibiotics, associated with increases in bacterial resistance, require new solutions, including materials with antibacterial properties. In this study, copper alginate fibers obtained using the classic wet method were used to make nonwovens which were modified with arginine-glycine-aspartic acid (RGD) derivatives. Stable polysaccharide-peptide conjugates formed by coupling with 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methylmorpholinium toluene-4-sulfonate (DMT/NMM/TosO−), and materials with physically embedded RGD derivatives, were obtained. The materials were found to be characterized by very high antibacterial activity against S. aureus and K. pneumoniae. Cytotoxicity studies confirmed that the materials are not cytotoxic. Copper alginate conjugates with RGD peptides have strong potential for use in regenerative medicine, due to their biocompatibility and innate antibacterial activity.