“There are Clinton people in the White House who clearly would like to see Hillary Clinton nominated,” Mr. Sanders said. “I understand that, and I simply hope that they will be as fair-minded as they can be,” he said, adding, “I take President Obama and Vice President Biden at their word, they’re not going to be tipping the scales here.”

The relationship between Mrs. Clinton and the White House is not without its own baggage. Her about-face on the trade deal angered Mr. Obama’s aides, especially given her previous vocal support for it. Some still recall the bitterness of her campaign against Mr. Obama in 2008. The president himself reacted to the trade deal shift with resignation rather than anger, aides said, viewing it as an understandable, if opportunistic, move.

The Clinton campaign is trying to smooth out future bumps by maintaining contacts at multiple levels, including high-level calls on policy between the campaign chairman, John Podesta, and the White House chief of staff, Denis R. McDonough, and routine check-in calls about public statements between the campaign’s communications director, Jennifer Palmieri, and her White House counterparts, Ms. Psaki and Mr. Earnest.

“If we’re going to do something we think we need to give them a heads-up on, Jennifer or I will call our former colleagues and let them know,” said Mr. Podesta, who was a senior Obama adviser before joining the Clinton campaign. “If we’re out on the campaign trail and rolling out a new policy, building on something he’s done or taking a position different than his, we’ll let him know we’re going to do it.”

Mrs. Clinton meets periodically with Mr. Obama, most recently last month when he invited her to the White House for a private 90-minute lunch the day after they each delivered speeches about how to confront the terrorist threat from the Islamic State. In her remarks, Mrs. Clinton portrayed the threat posed by the militant group in darker terms than the president and reiterated her proposal to enforce a no-fly zone over northern Syria to protect civilians, a step Mr. Obama has so far resisted.