Distributive alpha-N-methyltransferase that methylates the N-terminus of target proteins containing the N-terminal motif [Ala/Gly/Pro/Ser]-Pro-Lys when the initiator Met is cleaved. Specifically catalyzes mono-, di- or tri-methylation of the exposed alpha-amino group of the Ala, Gly or Ser residue in the [Ala/Gly/Ser]-Pro-Lys motif and mono- or di-methylation of Pro in the Pro-Pro-Lys motif. Some of the substrates may be primed by NTMT2-mediated monomethylation. Catalyzes the trimethylation of the N-terminal Gly in CENPA (after removal of Met-1). Responsible for the N-terminal methylation of KLHL31, MYL2, MYL3, RB1, RCC1, RPL23A and SET. Required during mitosis for normal bipolar spindle formation and chromosome segregation via its action on RCC1. N-terminal L-alanyl-L-prolyl-L-lysyl-[protein] + 3 S-adenosyl-L-methionine = 3 H(+) + N-terminal N,N,N-trimethyl-L-alanyl-L-prolyl-L-lysyl-[protein] + 3 S-adenosyl-L-homocysteine N-terminal L-seryl-L-prolyl-L-lysyl-[protein] + 3 S-adenosyl-L-methionine = 3 H(+) + N-terminal N,N,N-trimethyl-L-seryl-L-prolyl-L-lysyl-[protein] + 3 S-adenosyl-L-homocysteine N-terminal L-prolyl-L-prolyl-L-lysyl-[protein] + 2 S-adenosyl-L-methionine = 2 H(+) + N-terminal N,N-dimethyl-L-prolyl-L-prolyl-L-lysyl-[protein] + 2 S-adenosyl-L-homocysteine Predominantly nuclear. Belongs to the methyltransferase superfamily. NTM1 family.