Context : Single-dish observations of molecular tracers have suggested that both star formation and an AGN can drive the gas chemistry of the central \sim kpc of active galaxies . The irradiation by UV photons from an starburst or by X-rays from an AGN is expected to produce different signatures in molecular chemistry , which existing data on low- J lines can not distinguish , as they do not trace gas at high temperature and density . Depending on the angular scale of a galaxy , the observed low- J lines can be dominated by the emission coming from the starburst ring rather than from the central region . Aims : With the incorporation of high- J molecular lines , we aim to constrain the physical conditions of the dense gas in the central region of the Seyfert 2 galaxy NGC 1068 and to determine signatures of the AGN or the starburst contribution . Methods : We used the James Clerk Maxwell Telescope to observe the J =4–3 transition of HCN , HNC , and HCO ^ { + } , as well as the CN N _ { J } = 2 _ { 5 / 2 } -1 _ { 3 / 2 } and N _ { J } = 3 _ { 5 / 2 } -2 _ { 5 / 2 } , in NGC 1068 . We estimate the excitation conditions of HCN , HNC , and CN , based on the line intensity ratios and radiative transfer models . We discuss the results in the context of models of irradiation of the molecular gas by UV light and X-rays . Results : A first-order estimate leads to starburst contribution factors of 0.58 and 0.56 for the CN and HCN J =1–0 lines , respectively . We find that the bulk emission of HCN , HNC , CN , and the high- J HCO ^ { + } emerge from dense gas ( n ( H _ { 2 } ) \geq 10 ^ { 5 } ~ { } { cm ^ { -3 } } ) . However , the low- J HCO ^ { + } lines ( dominating the HCO ^ { + } column density ) trace less dense ( n ( H _ { 2 } ) < 10 ^ { 5 } ~ { } { cm ^ { -3 } } ) and colder ( T _ { K } \leq 20 K ) gas , whereas the high- J HCO ^ { + } emerges from warmer ( > 30 K ) gas than the other molecules . We also find that the HNC/HCN and CN/HCN line intensity ratios decrease with increasing rotational quantum number J . Conclusions : The HCO ^ { + } J =4–3 line intensity , compared with the lower transition lines and with the HCN J =4–3 line , support the influence of a local XDR environment . The estimated N ( { CN } ) / N ( { HCN } ) \sim 1 - 4 column density ratios are indicative of an XDR/AGN environment with a possible contribution of grain-surface chemistry induced by X-rays or shocks .