Methods are provided for suppressing the immune system response in recipients of transplanted organs, tissues or cells. An extracorporeal quantity of blood from the intended transplant recipient is treated to induce monocytes contained in the blood to differentiate and form dendritic cells. The maturation of the dendritic cells is truncated at a stage where the dendritic cells can inactivate T cell clones which would otherwise generate an undesired immune system response. The immature dendritic cells can be directly administered to the transplant recipient, or the dendritic cells can be co-incubated with the bone marrow or stem cell preparation, prior to transplantation, in order to suppress or eliminate anti-recipient donor T cells contaminating the bone marrow or stem cell preparation. The methods can be used to suppress graft versus host disease in recipients of transplanted bone marrow or stem cells, or to suppress rejection of transplanted organs or tissue.