General McMaster is viewed as more pragmatic than Mr. Flynn. He told his staff early on, for example, that he did not view the phrase “radical Islamic terrorism” as helpful. But that has not stopped Mr. Trump from using it in his speeches — a habit that shows the influence of Mr. Bannon, who views Iran and China as America’s great adversaries.

Unlike President Barack Obama, who used his first Nowruz message in 2009 to extend an olive branch to Tehran, Mr. Trump demonstrated no interest in engaging with Iran’s leadership. He did not mention Iran, let alone use its formal name, the Islamic Republic of Iran, as Mr. Obama did.

“This is a message designed to put the regime on the defensive,” said Dennis B. Ross, a former senior adviser to Mr. Obama on Iran. “It is smart and well crafted with clear messages in mind.”

Among those messages was one of reassurance to the Iranian diaspora, which has been affected by Mr. Trump’s executive order barring visitors from six predominantly Muslim countries, including Iran. In a few well-publicized cases, it sundered families that had hoped to get together for the holiday.

The statement praised Iranian-Americans as “one of the most successful immigrant groups in our country’s contemporary American history.” It made a point of noting that in addition to Islam, these immigrants come from Jewish, Christian, Zoroastrian and Bahai backgrounds — all religions that have faced some type of repression in postrevolution Iran.

Mr. Trump claimed “wonderful friendships with Iranian-Americans.” His director of Jewish outreach during the campaign was an Orthodox Jewish immigrant from Iran, David Peyman.