It is very clear that the Prime Minister wants Picard to "deal" with the issue at that point and it's not dealing with it by working to reintegrate those soldiers back into Angosian society.
Consider the possible situation had Picard given the Prime Minister a choice. They can either accept the Federation's help at reintegrating their soldiers back into society at no expense, or deal with the situation themselves. Taking sides in an armed conflict is one thing, but helping to prevent a conflict should be an entirely different matter, especially if this world has an interest in joining the Federation. Star Trek has done this kind of thing before!
Kirk: Yes, Councilman, you have a real war on your hands. You can either wage it with real weapons, or you might consider an alternative. Put an end to it. Make peace.
Anan: There can be no peace. Don't you see? We've admitted it to ourselves. We're a killer species. It's instinctive. It's the same with you. Your General Order Twenty Four.
Kirk: All right. It's instinctive. But the instinct can be fought. We're human beings with the blood of a million savage years on our hands, but we can stop it. We can admit that we're killers, but we're not going to kill today. That's all it takes. Knowing that we won't kill today. Contact Vendikar. I think you'll find that they're just as terrified, appalled, horrified as you are, that they'll do anything to avoid the alternative I've given you. Peace or utter destruction. It's up to you.
Fox: As a third party interested only in peace and the establishment of normal relations, I should be glad to offer my services as negotiator between you and Vendikar. I've had some small experiences in such matters.
Anan: There may be a chance. We have a direct channel with Vendikar's High Council. It hasn't been used in centuries.
Fox: Then it's long overdue.
See? That's the Federation working with a non-Federation civilization put an end to a conflict hands on. No "it's none of our business" or "Let's see if they survive the night".