The instructions, which were shown to The New York Times, stipulate that the Europeans agree to three key fixes: a commitment to renegotiate limits on missile testing by Iran; an assurance that inspectors have unfettered access to Iranian military bases; and an extension of the deal’s expiration dates to prevent Iran from resuming the production of nuclear fuel long after the current restrictions expire in 2030.

European diplomats said there was scope for an agreement on missiles and inspections, but not yet on the length of the deal. They argue that rewriting those terms would break the bargain they struck, not only with Iran but also with Russia and China, two other signatories. And breaching the deal, they say, would free Iran to pursue nuclear weapons again.

The upcoming talks are being led by Brian H. Hook, a low-key Republican lawyer who is the State Department’s director of policy planning, who has said he would bring the European request for a guarantee back to Washington. European diplomats said they worry that Mr. Trump’s scorn for the deal runs so deep that he would find other reasons to pull out. Last month, he warned that the accord “is under continuous review, and our participation can be canceled by me as president at any time.”

Even if Mr. Trump did pledge to abide by the deal, it is far from clear that a successor deal would be endorsed by Russia or China, let alone the Iranians, who signaled in recent weeks that they are planning a new project — a fleet of nuclear-powered ships, fueled by Iranian-made reactors — that they say would justify resuming the production of nuclear fuel as the limits imposed by the deal expire over the next dozen years.

Still, the mere fact that the United States and Europe are trying to work out a compromise attests to the desire, on both sides, to find a solution that would satisfy Mr. Trump while not unraveling the deal.