"Human solidarity is very visible, it's clear and across the world, people can feel the pain of those who are having to flee from war and persecution," Amnesty International Secretary General Salil Shetty told Reuters TV.
He said the results showed that most government responses to the refugee crisis were out of step with public opinion.
"(Citizens are) ready to reach out, and governments have to listen to the majority of the voices and not just a noisy few," said Shetty.
"We are facing a leadership crisis on this issue," he added. "We don't have many people like Angela Merkel, the Chancellor of Germany, who stood up in the face of some opposition to say this is an international human rights obligation."
Merkel has faced months of accusations of being too open to migrants, with Germany taking in 1.1 million migrants last year.
Almost all Germans surveyed and 87 percent of Britons said they would allow refugees into their countries.
But 17 percent of respondents said they should not be allowed into their country at all.
As the least welcoming country, 61 percent of Russians surveyed said they would not let refugees in.
Poland, Hungary and other former communist east European states say immigration, especially from the Muslim cultures of the Middle East, would disrupt their homogeneous societies.
Although 86 percent of Chinese participants agreed that governments should do more to help, the Chinese government remains reluctant to resettle refugees fleeing wars or persecution.
According to recent U.N. refugee agency (UNHCR) data, neither China, Russia or any Gulf states have resettled Syrian refugees since the war began.
The first-ever World Humanitarian Summit is being held in Istanbul next week as the number of people who have been forced from their homes globally hits record levels.
Aid agencies and campaigners will ask governments to commit to tackling forced displacement in a new way - that meets the immediate needs of the world's displaced, and builds their resilience and self-reliance.
UNHCR has said the number of people forcibly displaced worldwide was likely to have "far surpassed" a record 60 million in 2015, including 20 million refugees, driven by the Syrian war and other drawn-out conflicts.
(Reporting by Lin Taylor @linnytayls, Editing by Ros Russell; Please credit the Thomson Reuters Foundation, the charitable arm of Thomson Reuters that covers humanitarian news, conflicts, land rights, modern slavery and human trafficking, women's rights and climate change. Visit news.trust.org to see more stories)