DORAL, Fla. — Donald J. Trump said on Wednesday that he hoped Russian intelligence services had successfully hacked Hillary Clinton’s email, and encouraged them to publish whatever they may have stolen, essentially urging a foreign adversary to conduct cyberespionage against a former secretary of state.

“Russia, if you’re listening, I hope you’re able to find the 30,000 emails that are missing,” Mr. Trump said during a news conference here in an apparent reference to Mrs. Clinton’s deleted emails. “I think you will probably be rewarded mightily by our press.”

Mr. Trump’s call was another bizarre moment in the mystery of whether Vladimir V. Putin’s government has been seeking to influence the United States’ presidential race.

His comments came amid questions about the hacking of the Democratic National Committee’s computer servers, which American intelligence agencies have told the White House they have “high confidence” was the work of the Russian government.