Since Election Day, President-elect Donald J. Trump has proposed a U-turn in American diplomatic relations with Cuba, boasted about negotiations with a major manufacturer, trumpeted false claims about millions of illegal votes and hinted that he might upend current free speech laws by banning flag burning.

All in 140 characters or less.

As news organizations grapple with covering a commander in chief unlike any other, Mr. Trump’s Twitter account — a bully pulpit, propaganda weapon and attention magnet all rolled into one — has quickly emerged as a fresh journalistic challenge and a source of lively debate.

How to cover a president’s pronouncements when they are both provocative and maddeningly vague? Does an early-morning tweet amount to a planned shift in American policy? Should news outlets, as some readers argue, ignore clearly untrue tweets, rather than amplify falsehoods further?

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In interviews on Tuesday, political editors and reporters said that, for now, they planned to apply the same news judgment they would apply to any statement by a powerful leader, even as some acknowledged that social media allows Mr. Trump to reduce complicated subjects to snappy, and sometimes misleading, slogans and sound bites.