The Queen has urged people to find “common ground” and to respect “different points of view”.
Commentators have interpreted the remarks as a comment on the Brexit debate, with Parliament due to vote on the way forward next week and UK due to leave the EU on 29 March.
She was at an event to mark the 100 years of Sandringham Women’s Institute.
BBC royal correspondent Nicholas Witchell said there was little doubt the Queen was “sending a message”.
“It is impossible to imagine that the head of state would use a construction of words such as this without it being appreciated that they would be seen as a reference to the current political debate,” he said.
Her words echoed,
the theme of her Christmas broadcast our correspondent added.
As head of state, the Queen remains neutral on political matters and does not express her views on issues.
Speaking on an annual visit to the Women’s Institute near her estate in Sandringham, the Queen said: “The continued emphasis on patience, friendship, a strong community focus, and considering the needs of others, are as important today as they were when the group was founded all those years ago.
“Of course, every generation faces fresh challenges and opportunities.
“As we look for new answers in the modern age, I for one prefer the tried and tested recipes, like speaking well of each other and respecting different points of view; coming together to seek out the common ground; and never losing sight of the bigger picture.”
She said these approaches are “timeless, and I commend them to everyone”.
BBC political correspondent Laura Kuenssberg said that it was “not common” for the Queen’s remarks to be released in this way and it seemed “quite feasible” that the palace was trying to send a message to politicians.
Her Christmas message touched on the same issues, with the Queen saying: “Even with the most deeply held differences, treating the other person with respect and as a fellow human being is always a good first step towards greater understanding.”