Hedegaard is in the Marshall Islands this week for the Pacific Islands Forum (PIF), the first time she has visited low-lying atolls in the region which are threatened by rising sea levels.
"The sense of urgency is very clear and visible when you are here," she told AFP in an interview in the capital Majuro, which rises barely one metre (three feet) above sea level.
"Time is running out -- the world must get its act together. Those who are most vulnerable are getting very impatient for very good reasons."
She said the small island nations which form the bulk of the 15-nation PIF membership were leaders in adopting renewable energy, sending a powerful message to the rest of the world.
More From This Section
"It's quite impressive in this region to see (island) states, despite all their difficulties and limitations, actually starting to make the energy transition," she said.
"They have not created the climate problem, they are not the big culprits, but they know each of us has to do what we can."
The PIF nations will formally adopt a "Majuro Declaration" setting out ambitious climate targets tomorrow, then take it to the United Nations later in the month in the hope it can become a blueprint for other countries.
Some of the world's major polluters, including the United States, China, India and the EU are attending this week's summit, and Tuvalu Prime Minister Enele Sopoaga said the declaration would show them the world needs to act.
"That's the only way we can have globally agreed targets to reduce emissions of greenhouse gases," he added.
He also said the way small countries accessed funds from big donor nations for climate mitigation work needed to be streamlined so there was less red tape.