The United Nations' High Commissioner for Human Rights says the mounting evidence of military-perpetrated atrocities against Rohingya Muslims could constitute worldwide criminal law's most serious charge.
Zeid said some about 626,000 Rohingya have fled since August, and many more are continuing to pour into Bangladesh.
He told a special session of the Human Rights Council on the Rohingya on Tuesday: "My government is doing everything possible to deter these extremist acts".
The measure broke little new ground but did instruct the United Nations human rights office to assess the level of cooperation of Myanmar's government with United Nations rights monitors and other experts.
He listed a series of human rights abuses alleged to have taken place.
Myanmar's ambassador on the council denied the claims and said that his government was working with Bangladesh to help relocate those who had lost their homes.
"Given all of this, can anyone rule out that elements of genocide may be present?"
He added that UN agencies would be involved but stopped short of guaranteeing the immediate, unimpeded access to Myanmar for UN investigators that the UN has demanded.
Myanmar's government has denied allegations of ethnic cleansing and crimes against humanity, but it has refused United Nations investigators' and journalists' access to the affected areas in northern Rakhine state.
He urged the council to request that the UN General Assembly set up a mechanism "to assist individual criminal investigations of those responsible".
The UN first defined it in the Convention on the Prevention and Punishment of the Crime of Genocide in 1948.
The House called on Myanmar's leadership to end attacks on minorities in the northern Rakhine state.
Bangladeshi authorities have approved a plan to resettle about 100 thousand of Rohingya refugees on a desert flood-prone island Tanger Spell in the Bay of Bengal.