A charity that runs independent rescue boats to save refugees at sea said it had seen a 15-fold increase in donations in the past 24 hours, which it attributed to the international horror at the picture of a Syrian boy lying lifeless on a Turkish beach.

The Migrant Offshore Aid Station (MOAS) – set up by two philanthropists in Malta – said it had saved more than 10,000 lives during its first year in operation by giving medical and technical assistance to boats crossing the Mediterranean.

It told the Guardian it had seen individual donations hit €150,000 (£110,000) in the past 24 hours, with numbers climbing fast. Its previous highest day was €10,000.

The Guardian spent five days with the Migrant Offshore Aid Station (MOAS) meeting its crew and the people it saved. Guardian

MOAS said money was coming in from around the world whereas normally donors are restricted to Germany and other central European countries. “We never really saw so many come from the UK or US before, but now there are hundreds,” a spokesman said.

More than 2,000 individuals have donated to the charities in the 24 hours since the pictures of three-year-old Aylan Kurdi, who drowned with his five-year-old brother and their mother, appeared on newspaper front pages across the globe.

The MOAS director Martin Xuereb, a former commander of the armed forces in Malta, told the Guardian: “We think that the surge in donations is a direct response from people seeing this picture, many people feel very angry about the situation and they want to act.

“People are saying they don’t want to be bystanders anymore. We are increasingly understanding that behind every statistic, every number, there is a life, a life who has a mother, a father or a sibling, a grandparent.”

MOAS, which was set up by Maltese-based American philanthropist Christopher Catrambone and his Italian wife, Regina, owns a 40-metre expedition vessel as well as two search drones and two inflatable boats. It has a joint team of rescuers and paramedics with the charity Médecins Sans Frontières, who assist vessels which have got into difficulty, usually on the route between Libya and the Italian island of Lampedusa or Sicily.

Initially privately funded, the organisation began accepting donations from individuals this summer but said it had never before seen such interest in its work.

Xuereb said the image of the child on Bodrum beach, in the red T-shirt and sandals, had affected him personally. He also told how seeing the face of another child who died at sea had motivated him to continue his own humanitarian work.

“When I was working before MOAS, I was once there when workers opened a body bag, which I knew was a child, but I expected to see this angelic, sleeping face,” he recalled.

“But what I saw was a child in despair, his fist clenched, his eyes wide open when he died. I always think of that child, whenever I hear about the numbers who are dead.”

He added that he did not think people should see organisations like MOAS as the answer to the crisis. “We are a sticking plaster, we are not a solution. But what we are increasingly convinced of is that no one gets on one of those boats unless they feel they have no other choice.”