They also criticised the country's leader Aung San Suu Kyi - herself a Nobel Peace Prize victor - for what they called a lack of initiative to protect the Rohingyas.
He also requested the Myanmar government to urgently address the "root cause" of the problem in Rakhine State so that Rohingya Muslims do not have to seek shelter across the border. "Daw Suu Kyi is the leader and is the one with the primary responsibility to lead, and lead with courage, humanity and compassion", read the open letter.
Azeem Ibrahim is a Senior Fellow at the Center for Global Policy and the author of The Rohingyas: Inside Myanmar's Hidden Genocide.
Aung San Suu Kyi's Myanmar government has denied accusation of deploying excessive military force to respond to 9 October attack.
The signatories to the letter include business leader and philanthropist, Sir Richard Branson, BAFTA award victor and British film director, Richard Curtis, among 21 others.
Clashes have been continuing on and off in the region, especially since 9 October, when a police post was attacked near the border with Bangladesh by the ethnic armed men, killing nine security officers.
"Even if we do not receive a response, we will continue to sail as we believe this is an important humanitarian mission", he said.
She also recently met the foreign ministers of neighboring Southeast Asian nations and told them the Myanmar government is committed to resolving the issues in Rakhine State, but said "time and space are critical for the efforts to bear fruit", according to state newspaper The Global New Light of Myanmar. It would be one thing to round up suspects, interrogate them and put them on trial.
The letter, published on Thursday, accuses the Myanmar government of a "grossly disproportionate" military operation that has seen troops "unleash helicopter gunships on thousands of ordinary civilians.rape women and throw babies into a fire". The last major outbreak of violence in 2012 left hundreds dead and drove 140,000 people into internal displacement camps.
Urging the United Nations to do everything possible to encourage the government of Myanmar to lift all restrictions on humanitarian aid so that people receive emergency assistance, the global leaders said, "Access for journalists and human rights monitors should also be permitted, and an independent, worldwide inquiry to establish the truth about the current situation should be established". The group also asks that the Security Council make the Rohingya's plight a matter of urgency and that the United Nations secretary-general visit Myanmar in the coming weeks.
An estimated 150,000 to 200,000 Rohingyas, displaced by previous violence, live in Malaysia.
Calling on the worldwide community to rise to the occasion, the leaders said, "After Rwanda, world leaders [had] said "never again".