exhort
To strongly encourage someone to do the right thing.
To exhort means to strongly encourage or urge someone to do something, usually something good or important. When a coach exhorts her team at halftime to keep fighting even though they're behind, she's giving them a passionate, urgent push to give their best effort, speaking with intensity and conviction.
The word carries a sense of intensity and conviction. A teacher might exhort students to study hard before finals, or a parent might exhort a child to tell the truth about breaking a window. Leaders throughout history have exhorted their followers to stand up for what's right, work harder, or persevere through difficulties.
Exhortation is the noun form. Martin Luther King Jr.'s speeches contained powerful exhortations to pursue justice peacefully. When someone gives you an exhortation, they're not commanding you or threatening you. They're appealing to your better nature, trying to inspire you to rise to a challenge or do the right thing. The word suggests the speaker really believes in what they're saying and wants you to succeed.