The Arakan Rohingya Salvation Army (Arsa) announced a truce on Sunday, urging Myanmar's army to lay down weapons as well.
Sources said Muazzem Ali explained Bangladesh's situation and the pressure the country was facing due to migration of Rohingyas Muslims from Myanmar.
Amid a dramatic increase in the number of refugees fleeing violence in Myanmar's Northern Rakhine state, UNHCR called for urgent action to address the root causes of the recent surge in violence, so that people are no longer compelled to flee and can eventually return home in safety and dignity.
Thousands of displaced people in Rakhine have been stranded or left without food for weeks.
About 130,000 more Rohingya Muslims fled Myanmar from Bangladesh on Friday, almost doubling the count from earlier this week.
The Rohingya are an unrecognized Muslim minority in Myanmar, the country formerly known as Burma.
Arsa announced its ceasefire in a statement on Saturday.
Myanmar so far has made no public comments on the insurgents' initiative.
The refugees in Bangladesh are mostly women and children who have arrived on foot, the United Nations refugee agency said.
Most have walked for days and the United Nations says many are sick, exhausted and in desperate need of shelter, food and water.
The US State Department reacted to the Rohingya crisis on Friday, declaring: "Following serious allegations of human rights abuses including mass burnings of Rohingya villages and violence conducted by security forces and also armed civilians".
Rouhani slammed the inaction of worldwide organizations in this regard, saying "there needs to be more pressure on the government and army of Myanmar".
Bangladeshi border guards and villagers have told the BBC that they witnessed more than 100 Myanmar soldiers walking by and apparently planting landmines at the border.
The Muslim Rohingya minority community has always been subjected to discrimination in mostly Buddhist Myanmar, which denies them citizenship.
"We want to work with the governments of Myanmar and Bangladesh to prevent the humanitarian plight in the region", he said at the opening session of an Organization of Islamic Cooperation (OIC) summit in the Kazakh capital Astana.
Global aid programmes in Rakhine have been severely curtailed by the fighting in the state, but Myanmar authorities said on Saturday that they would set up three relief camps in Rohingya-majority areas.
Earlier this week, Myanmar's de facto leader Aung San Suu Kyi alleged a "huge iceberg of misinformation" was distorting the picture of the Rohingya crisis.