Degrades single-stranded DNA (ssDNA) in a highly processive manner. Also functions as a DNA deoxyribophosphodiesterase that releases deoxyribose-phosphate moieties following the cleavage of DNA at an apurinic/apyrimidinic (AP) site by either an AP endonuclease or AP lyase. Exonucleolytic cleavage in the 3'- to 5'-direction to yield nucleoside 5'-phosphates. Binds 2 Mg(2+) ions per monomer. Monomer. Interacts with ssb (via C-terminus); this interaction stimulates the exonuclease activity by recruiting the enzyme to its substrate. The N-terminal exonuclease domain and the exonuclease C-terminal domain form a central positively charged groove which binds the DNA.