Modern spark ignition internal combustion (IC) engines rely on highly diluted fuel-air mixtures to achieve high brake thermal efficiencies. To support this, new engine designs have introduced high stroke-to-bore ratios and cylinder head designs that promote high tumble flow and turbulence intensities. However, mixture dilution through exhaust gas recirculation (EGR) is limited by combustion instabilities manifested in the form of cycle-to-cycle variability. Propane has been observed to have superior EGR dilution tolerance than gasoline, which makes it a very competitive low-carbon fuel for the new IC engines without sacrificing efficiency. Two-dimensional direct numerical simulations (DNS) are performed with detailed chemistry to study and contrast the effect of turbulence intensity and dilution on propane and iso-octane premixed flames at high pressure conditions similar to those in-cylinder. A new reduced mechanism for propane consisting of 53 transported species and 17 quasi-steady state species is developed based on a previously published mechanism and used in these simulations. Three levels of turbulence intensity and two levels of exhaust gas dilution are chosen based on conditions relevant to IC engine operation. The DNS results are analyzed based on the evolution of the flame surface area and the statistics of its driving terms, which are found to be similar for both fuels when there is no dilution but considerably different under high dilution. The analysis of the DNS data provides fundamental insights into the underlying mechanisms for improved stability under dilution.