Much of the world looks to the US for a lead on "the most crucial issues that face our planet", Prince Charles has told its president George Bush.
Prince Charles and Camilla are not staying at the White House
In a post-dinner toast at the White House the prince said to Mr Bush: "Truly the burden of the world rests on your shoulders."
He and the Duchess of Cornwall were attending a banquet held in their honour on the second day of a US tour.
Mr Bush told guests the US drew "great strength" from the UK's friendship.
Prince Charles, who is well known for his views on the environment, noted the "enormous challenges" faced by Mr Bush.
"So many people throughout the world look to the United States for a lead on the most crucial issues that face our planet and indeed the lives of our grandchildren," he said.
Last week the prince told the BBC climate change should be seen as the "greatest challenge to face man" and treated as a much bigger priority in the UK.
He said climate change was "what really worried" him, adding that he did not want his future grandchildren to ask why he had not acted over the issue.
WHITE HOUSE DINNER
Celery Broth with Crispy Rock Shrimp
Medallions of Buffalo Tenderloin
Wild Rice Pancakes
Glazed Parsnips and Young Carrots
Mint Romaine Lettuce with Blood Orange Vinaigrette
Vermont Camembert Cheese and Spiced Walnuts
Petits Fours Cake
Chartreuse Ice Cream
The couple began their eight-day US tour in New York - where they visited Ground Zero - before flying into Andrews Air Force Base, outside Washington.
On Friday they will meet hurricane survivors in New Orleans.
US secretary of state Condoleezza Rice, former first lady Nancy Reagan and actor Kelsey Grammer were among around 100 guests at the dinner.
President Bush told his guests that their visit was a reminder of the unique and enduring bond between the UK and US.
WHITE HOUSE LUNCH
Watercress soup with applewood smoked bacon
Lemon sole with a herb crust
Lady apple sorbet in a brandy snap basket with spiced autumn fruit compote
He said: "The nation that defied bombardment from the air in 1940 once again refused to cower when its people were bombed from underground this summer.
"Your courage and fortitude are an inspiration to people throughout the world."
Prince Charles acknowledged the recent death of civil rights icon Rosa Parks.
"On the day that Rosa Parks was laid to rest there is a powerful message here about tolerance and inclusion that has relevance for the whole international community," he said.
A spokesperson for the prince described lunch as an informal affair and said subjects discussed included farming and the Bush family's desire to farm sustainably on their ranch.
After lunch, Laura Bush - the president's wife - accompanied Charles and Camilla to a Seed school, where they witnessed initiatives to tackle underachievement in disadvantaged areas.
The trio were met by about 100 pupils before joining a class of 12 and 13-year-olds and later planting a tree.
Prince Charles triumphantly held a spade aloft in response to cheers as he dug a small hole for the English Oak, Prince Valiant variety.
The trip is Prince Charles' and Camilla's first joint official overseas tour since they married.