Story highlights Trump tweeted several times Monday on the proposed travel ban from six Muslim-majority countries

Trump at one point was expected to nominate Conway to run the Justice Department's civil division

(CNN) George Conway, the husband of White House counselor Kellyanne Conway and one-time top contender of a key Justice Department job, took to Twitter Monday to criticize President Donald Trump for his morning travel ban tweets.

Trump tweeted several times on the proposed travel ban from six Muslim-majority countries, saying his Justice Department should not have submitted a "watered down, politically correct version" to the Supreme Court. The Justice Department has repeatedly tried to distance Trump's comments as President and during the campaign from its case looking to lift a legal ban against his executive order.

Later Monday, Conway said Trump hurt his case and made things difficult for the Office of Solicitor General, which argues cases before the Supreme Court.

"These tweets may make some ppl feel better, but they certainly won't help OSG get 5 votes in SCOTUS, which is what actually matters. Sad."

These tweets may make some ppl feel better, but they certainly won't help OSG get 5 votes in SCOTUS, which is what actually matters. Sad. https://t.co/zVhcyfm8Hr — George Conway (@gtconway3d) June 5, 2017

Conway confirmed to CNN that he sent the tweet.

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