When the philanthropist and cosmetics tycoon Leonard A. Lauder gave his trove of Cubist paintings, drawings and sculptures to the Metropolitan Museum of Art in 2013 — one of the most significant gifts in its history — the Met knew it would have to provide galleries of a quality commensurate with that of the collection.

As a result, hanging over the Met’s decision this year to postpone its new $600 million wing for Modern and contemporary art — as well as the museum’s recent management turmoil — have been nagging questions: Is Mr. Lauder’s gift, valued at more than $1 billion four years ago, now at risk? If the Met takes too long to resurrect the project or ultimately scales it back, might Mr. Lauder take his collection elsewhere?

Mr. Lauder, who agreed to answer these questions only through email, made clear that his initial donation of 78 works of art was never contingent on the Met’s construction of a new wing, nor was its future now in jeopardy.

“There is no issue with my gift,” he said. “We are aligned and I am confident that the Met will present the collection in a manner that is consistent with the excellence for which it is known.”