1) Explanation

Let's break down the sentence to understand the context and the meaning required for the blank:
- "Our government's commitment to democracy encourages many of the country's leaders to $\qquad$ despotic regimes in public pronouncements;"
- "Commitment to democracy" suggests a positive stance towards democratic principles and, by extension, a negative stance towards "despotic regimes" (tyrannical, oppressive governments).
- "In public pronouncements" implies that this action is visible and official.
- Therefore, the blank needs a word that means to criticize, condemn, or speak negatively about despotic regimes.
- "however, some of these same regimes have privately received aid from our government in the interest of national security."
- The "however" signals a contrast. Publicly, the leaders do one thing, but privately, the government does the opposite (provides aid to these regimes). This reinforces that the public action is one of condemnation or disapproval.

Therefore, the blank needs words that mean to strongly criticize or denounce.
Let's evaluate the given options:
- A. disparage: To regard or represent as being of little worth; belittle. This fits the idea of speaking negatively about despotic regimes.
- B. castigate: To reprimand (someone) severely. This also fits the idea of strongly criticizing or condemning.
- C. obviate: To remove a need or difficulty; avoid or prevent. This is unrelated to public pronouncements about regimes.
- D. eulogize: To praise highly in speech or writing. This is the opposite of what a democratic government would do to despotic regimes publicly.
- E. espouse: To adopt or support (a cause, belief, or way of life). This implies support, which is the opposite of the public stance.
- F. ameliorate: To make (something bad or unsatisfactory) better. This implies improving, not criticizing.

Conclusion:

The context clearly indicates that the government's democratic commitment would lead its leaders to publicly condemn or criticize despotic regimes. Both "disparage" and "castigate" convey this meaning of strong disapproval and criticism.

The final answer is $\(\mathrm{A}, \mathrm{B}\)$.