For months, President Donald Trump’s White House has been prone to veering off message. But it was crystal clear on one point Sunday: No one except Trump should put up a hand for the 2020 GOP ­presidential nod.

Vice President Mike Pence denied that he is considering a run for the presidency the next time around, issuing a statement, the vehemence of which underscored how sensitive the White House is to any questioning of whether Trump will seek a second term.

In what appeared to be a coordinated message, the White House also hit back Sunday at a New York Times report that described steps Pence and some GOP lawmakers have taken that could position themselves for presidential bids.

Pence went so far as to call the newspaper’s report “disgraceful and offensive.”

“The American people know that I could not be more honored to be working side by side with a president who is making America great again,” the vice president said.

“Whatever fake news may come our way,” he said, citing another favored presidential phrase, “my entire team will continue to focus all our efforts to advance the president’s agenda and see him ­re-elected in 2020.”

Trump began raising money for a 2020 campaign almost immediately upon taking office, but a re-election bid would face several potential obstacles:

At 71 now, Trump would be the oldest second-term chief executive were he to win the 2020 election.

In addition, his approval ratings are at a low unprecedented at this point in a presidential term.

Moreover, an increasingly complex special counsel investigation, looking at whether Trump’s campaign cooperated with Kremlin interference in the 2016 race, has been gathering momentum. Special counsel Robert Mueller recently began working with a grand jury in Washington.

Deputy Attorney General Rod Rosenstein, to whom Mueller reports because Attorney General Jeff Sessions has recused himself from Russia-related matters, said Mueller would be guided by the emerging evidence, wherever it takes him, and implicitly rebutted Trump’s accusation that the entire matter is a “fraud.”

“The special counsel is subject to the rules and regulations of the Department of Justice, and we don’t engage in fishing expeditions,” Rosenstein said on “Fox News Sunday.” Mueller could seek authorization to broaden the scope of the probe if he deemed it necessary, Rosenstein said.

He also commented on the Justice Department’s announcement Friday that it was stepping up investigations of leaks of classified information. He appeared to at least partly pull back from Sessions’ suggestion that prosecutors might pursue reporters for stories they’ve published.

“The attorney general has been very clear that we’re after the leakers, not the journalists. We’re after the people who are committing a crime,” Rosenstein said. “We don’t prosecute journalists for doing their jobs.”

“Generally speaking, reporters who publish information are not committing a crime,” he said, although he added that “there might be a circumstance where they do.”

The move to increase leak investigations appears to have placated Trump, who in recent weeks publicly disparaged both Sessions and Rosenstein.