What is the word for what someone is doing when they say, "Don't worry", or "Cheer up"?

When someone tells you, "Don't worry," or "Cheer up," that's sort of like commanding you, but not really? Is there a verb like "command" that indicates what they're doing, either transitive or intransitive?

He reassured me, "Don't worry."

He consoled me, "Cheer up."

I'm looking for a verb that would work for both.

I originally included "Be well" in my question, but as it has been pointed out to me, "Be well" is more of a nicety that carries no hint at all of an imperative. I would also add "Relax" or "Calm down" to the examples, but as has been pointed out, those can carry some demeaning connotations.

My sample sentence is,

After catching his breath, he admonished(?) them, "Don't worry guys, problem solved."

• The criteria for an accepted word: I'm looking for a word more specific than "say", softer than "command" (even softer than "admonish", but that's the best I've heard so far), and applicable to both examples above.

• Words I didn't like, besides those I've mentioned:

  • tell, say: too generic
  • reassure: not applicable to both cases
  • counsel, admonish: as others have indicated, the typical connotations make them less than ideal
• I did a thesaurus search on command and exhort; seeing the synonyms listed for these two, I realized that I don't recall ever having heard a word that could apply — admittedly, my recall isn't great, but ELU seemed like a good place to turn

encourage , encouraging, encouragement

Edwin Ashworth mentioned that one example was a form of -encouragement- in comments ... I think it has broad enough meaning to apply to any words that are meant to improve another person's outlook

google definition of encourage

en·cour·age - verb

• give support, confidence, or hope to (someone).

"we were encouraged by the success of this venture"

synonyms: hearten, cheer, buoy up, uplift, inspire, motivate, spur on, stir, stir up, fire up, stimulate, invigorate, vitalize, revitalize, embolden, fortify, rally; More

• give support and advice to (someone) so that they will do or continue to do something. "pupils are encouraged to be creative"

synonyms: persuade, coax, urge, press, push, pressure, pressurize, prod, goad, egg on, prompt, influence, sway; informalput ideas into one's head

"she had encouraged him to go"

• help or stimulate (an activity, state, or view) to develop.

"the intention is to encourage new writing talent"

synonyms: support, back, champion, promote, further, foster, nurture, cultivate, strengthen, stimulate; More