Phrase: Trust me on that?

[Jibja]

If someone has asked me to do something, can I reply with this sentence?

"Trust me on that"

I'm not so sure about the preposition "on" whether it is the right one to be used here?

[Yankee]

Hi Jibja

In my opinion, a more likely response for the situation you mentioned would be "You can count on me".

I would normally expect the expression "Trust me on that" to have a meaning similar to "You should believe what I told you" or "Believe me -- what I told you is true".
.
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"Nearly all men can stand adversity, but if you want to test a man's character, give him power." ~ Abraham Lincoln

[Jibja]

Thanks so much Yankee.