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Donald J. Trump said on Wednesday that he expected to reveal his vice presidential pick sometime in July — before the Republican National Convention in Cleveland — but added that he would soon announce a committee to handle the selection process, which would include Dr. Ben Carson.

Mr. Trump made the comments in an interview with The New York Times the morning after he became the presumptive Republican Party nominee for president, facing only Gov. John Kasich of Ohio in the G.O.P. race.

Mr. Trump, the Manhattan businessman, said that while he was not committed to making a more conventional political pick in the form of a seasoned politician, he was leaning in that direction.

“I’m more inclined to go with a political person,” Mr. Trump said. “I have business very much covered.”

He added, “I think I’ll be absolutely great on the military and military strategy.”

But the vice presidential choice will probably not come until July, Mr. Trump said. As for the process used to make the selection, he said, “I’ll set up a committee, and that I will do soon.”

“I think on the committee I’ll have Dr. Ben Carson and some other folks,” Mr. Trump said.

Despite the fact that he has said generally nice things about Mr. Kasich, the governor of a crucial battleground state, Mr. Trump said that the governor was not currently on his short list. “Not at this moment,” Mr. Trump said.

He also questioned why Mr. Kasich, who has been mathematically eliminated from getting the 1,237 delegates needed to secure the nomination, is remaining in the race through the June 7 primary in California.

“I guess he likes the food in California,” Mr. Trump said. “The whole thing is ridiculous.”