"Thank God" vs "Thanks God"

Which is more appropriate/correct?

Thank God for His grace and mercy on […].
Thanks God for His grace and mercy on […].

The person is expressing his/her thankfulness to God. Thank God seems better, but it sounds a bit like lucky.

I could rephrase it as "Thanks be to God for […]." which is the intended meaning. I am just looking for the correct short way to say that.

The first sentence is fine as a statement that you are thanking God. It's short for "I thank God for his grace and mercy..." It's not a prayer only because you are not actually addressing God, but it could be part of a conversation, discussion, testimonial in church, etc.

The second sentence doesn't work quite right. If you are literally saying "Thanks" to God, as in you are offering a prayer to God and are speaking to him/her, then you will want to to say "Thanks, God, for your grace and mercy..."
If you want more formality, as in "Thanks be to God for ..." that's fine, but what you have is also fine, with the small changes.

Thank God!

is the correct way of expressing gratitute to God. It's one of the rare cases of legitimate use of the Subjunctive Mood.

'Thanks God' is possible in the Indicative Mood (3rd person)

My sister thanks God every day for [insert reason to thank God here].

When your friend Jim does you a favor, you can thank him:

Thanks, Jim!

The same way it's technically possible to say:

Thanks, God!

as an informal way of saying 'thank you' to God, as though you were speaking with him/her in person. Note the use of the comma.