Melting temperatures of sodium and potassium to 110 and 145 kbar, respectively, were determined by optical property changes with an externally heated diamond anvil cell using mineral oil as the pressure medium. The pressure was obtained from the known pressure and temperature shifts of the ruby fluorescence line. Sodium shows a continuous rise in the melting temperatures with pressure. The melting temperature of potassium remains nearly constant above about 70 kbar and the melting curve changes its slope drastically at 110 kbar. This is attributed to the bcc-fcc phase transformation that has been recently reported at room temperature around 110 kbar using the diamond anvil technique.