“Nobody wants a major-power war,” General McMaster told reporters. He also said Mr. Trump wants to try to identify potential areas of cooperation with Russia, be it on de-escalating the conflict in Syria, addressing the nuclear threat from North Korea or confronting transnational terrorist threats.

Beyond those general themes, Mr. Trump’s advisers have yet to devise a set of talking points for the closely watched meeting, a process made all the more difficult given the cloud of suspicion hanging over the president and his own propensity to go off-script.

It is rare and potentially risky for an American president to go into such a consequential meeting with another world leader — particularly one like Mr. Putin, a forceful and persuasive figure — with so little preparation on what policy objectives he wants to pursue, said Michael A. McFaul, who served as the United States ambassador to Russia under President Barack Obama.

“Mr. Trump may not be preparing in terms of deliverables or outcomes that he seeks, but you can bet that Mr. Putin is,” said Mr. McFaul, who as the chief Russia specialist at the National Security Council in 2009 prepared Mr. Obama for his first meeting with then-President Dmitry A. Medvedev of Russia.

“The big danger with Trump and his instincts is that he often defines a ‘good meeting’ or a friendly encounter as a positive outcome of a meeting with a head of state, and with Putin — where we have a big agenda, and a lot of it’s adversarial — he’s got that backward,” Mr. McFaul said.

Representative Adam B. Schiff of California, the top Democrat on the House intelligence committee, said it was crucial that the meeting be “more than a grip-and-grin,” particularly given Mr. Trump’s unwillingness to acknowledge Russia’s efforts to sway the election.