Use "insist" in those two sentences. 'Persist' means 'carry on doing something, in spite of anything'; if you express the thing (something) you can use it like this: He persisted in his claim that he was innocent, but "persist" on its own doesn't convey any sense of saying or writing something (as "insist" does) - He insisted on his innocence means the same.
There is another meaning of "insist" - "require as a matter of strict habit": He insisted on two eggs, lightly boiled, for breakfast. You would not use "persist" in this case, unless something happened that would lead one to expect a change: Even after the lottery win, he persisted in his habit of walking to work - in this case he would be persisting in insisting!
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