Abstract To assess the properties of the quark–gluon plasma formed in ultrarelativistic ion collisions, the ATLAS experiment at the LHC measures a correlation between the mean transverse momentum and the flow harmonics. The analysis uses data samples of lead–lead and proton–lead collisions obtained at the centre-of-mass energy per nucleon pair of 5.02 TeV, corresponding to total integrated luminosities of $$22~\upmu \text {b}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>22</mml:mn><mml:mspace/><mml:mi>μ</mml:mi><mml:msup><mml:mtext>b</mml:mtext><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> and $$28~\text {nb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>28</mml:mn><mml:mspace/><mml:msup><mml:mtext>nb</mml:mtext><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> , respectively. The measurement is performed using a modified Pearson correlation coefficient with the charged-particle tracks on an event-by-event basis. The modified Pearson correlation coefficients for the 2nd-, 3rd-, and 4th-order flow harmonics are measured in the lead–lead collisions as a function of event centrality quantified as the number of charged particles or the number of nucleons participating in the collision. The measurements are performed for several intervals of the charged-particle transverse momentum. The correlation coefficients for all studied harmonics exhibit a strong centrality evolution, which only weakly depends on the charged-particle momentum range. In the proton–lead collisions, the modified Pearson correlation coefficient measured for the 2nd-order flow harmonics shows only weak centrality dependence. The lead-lead data is qualitatively described by the predictions based on the hydrodynamical model.