Q. If one has the opportunity to see a president or a prime minister does he make a special blessing?
If not should one recite without the name of Hashem?
A. In question 173, If it is halachically appropriate to recite a blessing on seeing Prince Charles or Queen Elizabeth, we wrote: "Shulchan Aruch( O.H. 224: 8) quotes the Talmud (Brochos 58a): “On Gentile Kings one blesses “He bestowed from His glory to flesh and blood”. Mishna Berurah (ibid. 8) rules that you only recite the full blessing (mentioning Hashem’s name), if the sovereign has absolute power including life and death decisions, otherwise you bless omitting Hashem’s name.
Birchas Hamedaver (p. 404) quotes opinions that include in the full blessing, a president or leader that is empowered to grant a pardon to a death-convicted individual.
Many Poiskim maintain that the blessing is recited only if the monarch is dressed in distinctive royal or official attire. (Tshuvos Vehanhogos 2: 139, Tzitz Eliezer 22: 14 et al.)
Horav Shlomo Miller’s Shlit”a opinion is that on Prince Charles no brocho need be recited meantime. On the Queen you can recite without Hashem’s name."
However, on question 1548 in regard to meeting with President Trump we wrote: "Horav Shlomo Miller’s Shlit’a opinion is that because of the character and nature of the prevalent democracy, the Presidency of the U.S., has become so open to criticism, disparagement and condemnation, even when unwarranted and gratuitous. Therefore it would hardly qualify as an honour comparable to the Creator’s, and no brocho at all should be recited."
The Rov maintains that a similar ruling may apply nowadays to a prime minister.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a