According to the agreement, which was finalised in Myanmar's capital Naypyidaw, a two-year deadline has been set for the repatriation of the Rohingyas.
Ali briefed Swaraj about the deal, the statement said.
"That's completely counterproductive", Nauert said while responding to a question on the agreement reached between Bangladesh and Myanmar on the repatriation of the Rohingyas.
Rohingya communities from across the globe have demanded that the Rohingya refugees sheltering in Bangladesh be guaranteed security of life and property and peaceful coexistence as equals with all other people in Myanmar before they are repatriated.
The ministry said a joint working group from the two countries finalized an agreement on Monday on the physical arrangements for the repatriation of the ethnic Rohingya.
A spokesperson from the un high commission for refugees said Myanmar also needed to address the underlying causes of the crisis and that refugees should only return when they feel it is safe for them.
The UN refugee agency said it is not involved in the process but is willing to play a "constructive role" in the process if allowed, specifically in registering the refugees and helping determining whether they are returning to Burma voluntarily.
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Communal tension between the Buddhist Rakhine population and Muslim Rohingya has risen sharply in recent years.
Speaking to SkyNews, Twigg said: "We need massive reassurances before there can be any suggestion of refugees returning and any return must be genuinely voluntary".
The United Nations estimates that more than 650,000 Rohingya refugees have fled to Bangladesh since August of a year ago to avoid violence and the military crackdown in Rakhine.
Bangladeshi foreign secretary Mdshahidul Haque said the government had wanted Myanmar to accept 15,000 Rohingya each week - however, they eventually settled on 300 a day.
It is risky that the regime has already claimed state-ownership of Rohingyas' land within the affected region of northern Rakhine State, said the statement, signed by 15 Rohingya organisations including from the UK, USA, Denmark, Japan, Australia, Canada, Malaysia, Germany, Switzerland, Finland, Italy, Sweden, Norway and Netherlands.
"Security forces asked them to disperse and fired warning shots with rubber bullets. but they didn't stop, so police had to use real bullets", Myanmar police spokesman Colonel Myo Soe told AFP.