Carbon nanotubes (CNTs) are widely used in high-quality and high-performance nanoscale devices. Using first-principles calculations, we studied the interaction at the interface between parallel CNTs with different electrical properties under applied transverse electric fields. Typical metallic armchairs (6,6) and semiconducting zigzag (10,0) CNTs were considered. The effect of axial moving of one of the CNTs on the interface electronic structure and interaction energy for different interface types was analyzed. Our calculations revealed that interfacial adhesion of CNTs increased with the increase of the external electric field. At this, the interface charge redistribution for (6,6) and (10,0) CNTs showed different polarization responses. By analyzing the density of states (DOS), a correlation between the semiconductor-to-metal transition in parallel (10,0) CNTs and interface interaction under applied external electric field was demonstrated. Obtained results provide a theoretical background for the application of the adhesion properties of CNTs in future nanoscale devices.