Donald J. Trump has repeatedly promised a “pivot” toward a softer, gentler, more refined version of his candidacy since he emerged as the presumptive Republican nominee. But on Monday, Mr. Trump’s television interviews and speeches made clear that such a pivot would never come.

In four morning interviews, Mr. Trump stood by his ban on Muslim immigrants and said that President Obama was incompetent or knew much more than he was letting on about the type of terrorist threat the country faces. That statement, which Mr. Trump declined to completely clarify in a statement to Bloomberg Politics late in the day, was taken by some as implying that Mr. Obama, whose critics have tried to smear him as a Muslim in disguise, was sympathetic to terrorists.

Later in the day, in a speech in New Hampshire, Mr. Trump expanded on his proposed immigration ban and also called for large-scale surveillance of activities of Muslims in the country.

The speech was a stark contrast to one delivered shortly before by Hillary Clinton, who made no direct mention of Mr. Trump and urged the type of conciliatory notes that the nation struck immediately after the Sept. 11, 2001, terrorist attacks. She made a muscular defense argument, similar to the one Mr. Trump struck, but she proposed a more globalist view of the world than he did.