In some embodiments, the disclosure relates generally to methods, as well as related compositions and kits for recombinase-mediated nucleic acid amplification, such as recombinase-polymerase amplification (RPA), of a nucleic acid template using at least one blocked primer that contains a 5′ domain, at least one nucleotide that is cleavable by an RNase H enzyme, a 3′ domain, wherein the primer is not extendable by a polymerase, and wherein the 3′ domain has a length of 7-100 nucleotides, for example 10-30 nucleotides. These methods and the use of a blocked primer reduce or eliminate non-specific amplification products, such as primer dimers, which are generated in RPA reactions.