The full-page advertisement was published in News Corp and Fairfax newspapers urging Mr. Wilkie to report any information in his possession to proper authorities, The Australian reported.
Alexander said he was "angered and disappointed by the outrageous allegations" made by Mr. Wilkie.
The allegations also included claims that Crown allowed the use of illicit drugs at the casino, covered up domestic violence, and had avoided scrutiny by the money movement watchdog AUSTRAC of transactions over $10,000.
"Mr Wilkie has said he does not know if the allegations he has referred to, and repeated, are in fact true," Mr. Alexander said in the open letter.
"If he believes he has evidence of wrongdoing, he should stop the political games, step out of the parliament and make his claims without privilege.
"He should also report any information he has in his possession directly to the relevant authorities."