A new variant of the effective pomeron exchange model is proposed for the description of the correlation, observed in pp and pp collisions at center-of-mass energy from SPS to LHC, between mean transverse momentum and charged particles multiplicity. The model is based on the Regge- Gribov approach. Smooth logarithmic growth with the collision energy was established for the parameter k, the mean rapidity density of charged particles produced by a single string. It was obtained in the model by the fitting of the available experimental data on charged particles rapidity density in pp and pp collisions. The main effect of the model, a gradual onset of string collectivity with the growth of collision energy, is accounted by a free parameter b that is responsible in an effective way for the string fusion phenomenon. Another free parameter, t, is used to define string tension. We extract parameters β and t from the available experimental results on p_t- multiplicity correlation at nucleon collision energy p s from 17 GeV to 7 TeV. Smooth dependence of both β and t on energy allows to make predictions for the correlation behavior at the collision energy of 14 TeV. The indications to the string interaction effects in high multiplicity events in pp collisions at the LHC energies are also discussed.