The resolution passed the committee by consensus, meaning under General Assembly rules the body will unanimously pass it later this year.
Myanmar emerged from a half-century of military rule in 2011, but its transition to democracy has been marred by sectarian violence that has left more than 240 people dead and sent another 240,000 fleeing their homes, most of them Rohingya.
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Some say the inter-communal violence presents a threat to Myanmar's political reforms because it could encourage security forces to re-assert control.
In 1982, Myanmar passed a citizenship law recognizing eight races and 130 minority groups but omitted the nation's 800,000 Rohingya, among Myanmar's 60 million people.
Many Myanmar Buddhists view the Rohingya as interlopers brought in by British colonialists from modern-day Bangladesh, but many Rohingya say they have lived in the country once known as Burma for hundreds of years.
Nobel Peace Prize laureate Aung San Suu Kyi, seen as likely to be elected as the next president of Myanmar, has had little else to say about Rohingya rights. She declined to meet with an Organization of the Islamic Conference delegation visiting Myanmar this week to look into the plight of the Rohingya.
Myanmar had been ostracized by most of the world for 50 years after a coup that instituted military rule. But in recent years the nation has been cautiously welcomed into the international community after it freed many political prisoners and ended the house arrest of Syu Kyi and instituted reforms.
President Barack Obama visited the country last year on an Asian tour, as a hallmark of Myanmar's rehabilitation.
The General Assembly resolution welcomed a statement by Myanmar's president that "no prisoners of conscience will remain in prison by the end of the year." Myanmar released 69 political prisoners last week.