More than 420,000 Rohingya refugees have fled from Myanmar to Bangladesh in less than a month, with most ending up in camps in the Bangladeshi district of Cox's Bazar, which already had hundreds of thousands of Rohingya refugees who had fled prior rounds of violence in Myanmar.
Mr Grandi was speaking while touring refugee camps at Cox's Bazar, Bangladesh. 'I was struck by the incredible magnitude of their needs.
Grandi said an "incredible outpouring of local generosity" needs to be "beefed up by massive worldwide assistance, financial and material".
Ufuk Uyan, general manager of the Islamic finance bank, said their employees and customers offered to help the Rohingya with the hope this will pave way for charity campaigns. "That's partly why I am here, to help... the government organize that response".
The home minister said India would not be violating any global law if it deports Rohingyas as it is not a signatory to the UN Refugees Convention 1951. The government also said if allowed to stay, they would exhaust the natural resources meant for Indian citizens that could culminate in hostility towards them and lead to social tension.
He said the US welcomed Myanmar leader Aung San Suu Kyi's decision to speak publicly about the problem this week.
Some 40,000 Rohingyas have settled in India, and 16,000 of them have received refugee documentation, the United Nations estimates.
"By virtue of customary law, its ratification of the International Covenant on Civil and Political Rights, the obligations of due process and the universal principle of non-refoulement, India can not carry out collective expulsions, or return people to a place where they risk torture or other serious violations", he said.
Bangladesh already prohibits the sale of SIM cards to its own citizens who can not provide an official identity card, in a bid to frustrate the organisational capacity of home-grown militants. The process is expected to take several months to complete.
Turkey has been at the forefront of providing aid to Rohingya refugees and President Recep Tayyip Erdogan raised the issue with the UN. They have also asked for the government and the army to facilitate humanitarian aid for displaced persons.
The Rohingya, a stateless Muslim minority, are reviled in Buddhist Myanmar where they are regarded as illegal immigrants.
The minority group has been facing an escalated campaign of horrific violence since late a year ago, when the military laid siege to Rakhine.
UNICEF estimates suggest an "unprecedented" 60 per cent of new refugees in Bangladesh are children while Rohingya girls are exposed to risks of sexual violence and early marriage.