Troy Jackson, who is set to become the party's nominee, also said in an interview that he was not sure he wanted the support of Senator Chuck Schumer in the general election.
The White House press secretary said the unspecified "enhancements" would take place this fall. The plane has been under scrutiny over whether it has sufficient defensive capabilities.
Some Democrats condemned the New York City mayor after he said his staff was discussing whether to arrest the Israeli prime minister when he arrives for the U.N. General Assembly.