adjective / noun
earnest
UR-nist/ˈɜːrnɪst/
Seriousness and sincerity in purpose or manner.
The young man makes an earnest appeal, maintaining steady eye contact with the older listener.

Etymology
Old English eornoste meant “zealous, serious”; the word may instead come from the related noun meaning “serious intent.” Both connect earnestness with genuine purpose, not merely a solemn manner.
In context
I would call on them, in the most earnest manner, to consider this as an affair of the utmost importance to themselves.
More examples
- His earnest apology convinces me that he regrets his mistake.
- I'm in earnest when I say we need help.
- They are earnest about improving conditions at the shelter.
Forms
earnest · more earnest · most earnest
earnestly adverb — In a serious and sincere manner.
earnestness noun — The quality of being serious and sincere.