He told Science, the "house magazine" of the US scientific establishment: "As the world's only remaining superpower, the United States is accustomed to leading internationally co-ordinated action.
"But at present the US Government is failing to take up the challenge of global warming."
In Britain, the number of people at high risk of flooding was expected to more than double to nearly 3.5 million by 2080, Sir David said.
And damage to properties could run to tens of billions of pounds every year.
Britain was trying to show leadership by cutting energy consumption and increasing the use of renewable sources, Sir David added.
But the UK was responsible for only about 2% of the world's emissions while the US, with just 4% of the world's population, produced more than 20%.
The UK was asking the world's developed economies to cut greenhouse gas emissions by 60% of 1990 levels by about 2050, under the United Nations Framework Convention on Climate Change (UNFCC), Sir David said.
But despite declaring support for the UNFCC's objectives, the US had failed to ratify the Kyoto accord for emission reductions and "refused to countenance any remedial action now or in the future".
Sir David added: "We can only overcome this challenge by facing it together, shoulder to shoulder.
"We in the rest of the world are now looking to the USA to play its leading part."
Sir David said climate change was the most severe problem faced by the world.
"The United States is already in the forefront of the science and technology of global change, and the next step is surely to tackle emissions control too," he said.
"If we do not begin now, more substantial, more disruptive, and more expensive change will be needed later on."
Levels of carbon dioxide and other greenhouse gases in the atmosphere have risen steeply since the industrial revolution.
Concentrations have increased mainly because of the use of fossil fuels, deforestation and other human activities, spurred on by economic and population growth.
Greenhouse gases stop energy escaping from the Earth's surface and atmosphere.
If levels rise too high, excessive warming can distort natural patterns of climate, researchers say.
Climate change is the most severe problem we are facing today
The United States is already in the forefront of the science and technology of global change, and the next step is surely to tackle emissions control too