Provided are methods for producing circular deoxyribonucleic acids (DNAs). In some aspects, the methods include amplifying a target nucleic acid using forward and reverse primers each comprising a 5 phosphate group, a 5 overhang region, a 3 hybridization region that hybridizes to the target nucleic acid, and a uracil disposed between the 5 overhang region and the 3 hybridization region. The amplifying produces amplicon pairs comprising phosphorylated 5 overhangs to which adapter nucleic acids are ligated to produce a circular DNA. In other aspects, the methods comprise amplifying a target nucleic acid using forward and reverse primers each comprising first and second stem regions complementary to each other and separated by a linker region. According to such methods, the resulting amplicons are combined with an exonuclease, a DNA polymerase and a DNA ligase under conditions in which circular DNAs are produced. Related compositions and kits are also provided.