S-adenosyl-L-methionine-dependent methyltransferase that mediates mRNA cap1 2'-O-ribose methylation to the 5'-cap structure of mRNAs. Methylates the ribose of the first nucleotide of a m(7)GpppG- capped mRNA and small nuclear RNA (snRNA) to produce m(7)GpppRm (cap1). Displays a preference for cap0 transcripts. Cap1 modification is linked to higher levels of translation. May be involved in the interferon response pathway. {ECO:0000269|PubMed:18533109, ECO:0000269|PubMed:20713356, ECO:0000269|PubMed:21310715}. This is the function of Ensembl gene identifier ENSG00000137200 (CMTR1, cap methyltransferase 1).