(CNN) President Donald Trump's approval rating and re-election support remain strong among Iowa's registered Republicans, but a sizable minority of the party's registrants say they hope the president faces a challenger in the 2020 caucuses.

The new CNN/Des Moines Register/Mediacom poll of registered Republicans in Iowa finds 81% approve of the way the President is handling his job, unchanged since December, and 82% say they have a favorable view of Trump, up 5 points in that time. Roughly two-thirds (67%) say they'll definitely vote to re-elect the president, and about 6 in 10 (59%) are at least fairly confident he'll win in 2020.

But those positive signs are tempered by some registered Republicans' hope for a challenger to the President. Overall, Republicans are about evenly divided on the question, with 40% saying they hope the President faces a challenger from the party in the caucuses, and 41% saying they hope he does not face one. Another 19% are unsure.

Those who hope for a challenger to the President are generally positive about Trump, but they are less positive than their fellow registered Republicans about the President's performance in office (63% say they approve vs. 97% among those who say they hope Trump is not challenged) and in their impressions of him generally (66% view him favorably vs. 95% who hope he's not challenged).

Looking to 2020, however, they are far less likely to say they will definitely vote for his re-election (38% say so compared with 92% of those who do not want to see him face a GOP challenger). And most have doubts about whether he can win a second term: 56% in this group say they are only somewhat confident he'll win or are almost certain he'll lose, compared with fewer than 2 in 10 of those who say they don't want to see the president challenged from inside the party.

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