Nearly 125,000 Rohingya refugees - mostly women and children - have crossed the border into Bangladesh in the past 11 days, fleeing a security sweep by Myanmar forces who have been torching villages in response to alleged attacks by Rohingya fighters.
Since the latest round of violence began on August 25, at least 400 people have been killed in the ensuing clashes and a military counter-offensive.
"The grievances and unresolved plight of the Rohingya have festered for far too long and are becoming an undeniable factor in regional destabilisation," Guterres told reporters at the United Nations headquarters in New York on Tuesday.
"The authorities in Myanmar must take determined action to put an end to this vicious cycle of violence and to provide security and assistance to all those in need," he added.
Guterres also urged the UN Security Council to press for calm, sending the 15-member body a rare letter saying that "the international community has a responsibility to undertake concerted efforts to prevent further escalation of the crisis."
Al Jazeera's James Bays, reporting from the UN headquarters in New York, said: "There is a real concern from the UN about the humanitarian situation because of this human exodus and the sheer number of people crossing the border into Bangladesh."
The UN chief last week had urged restraint by security forces to avoid a humanitarian catastrophe from the refugee exodus, but he stepped up the pressure on Tuesday.
The UN Security Council met last week to discuss the crisis, but there was no formal statement following the closed-door meeting.
"Following this letter by Guterres, we are likely to see another meeting of the council pretty soon," said Bays.
The UN's refugee agency, UNHCR, also voiced grave concern for the safety of Rohingya Muslims fleeing to Bangladesh.
"Some reported that their family members were burned, or shot or slashed to death," said Duniya Khan, UNHCR spokeswoman.
"During their flight, many fled into the jungles or mountains, hiding and walking for days before they reached land or river and to cross the border."
She added: "Some of them also told us that they've been walking for three days, and they didn't have anything to eat, other than the rain water or the water on grounds."
The Rohingya are seen as illegal immigrants in mainly-Buddhist Myanmar and have suffered decades of persecution, according to rights groups.
They have been forced to live under apartheid-like restrictions on movement and citizenship.
The UN has repeatedly called on Myanmar to grant the Rohingya rights, and a recent UN report said the brutal crackdown against the Muslim minority could amount to crimes against humanity.
Guterres said on Tuesday that Myanmar's government must grant the Rohingya "either nationality or at least, for now, a legal status that will allow them to have a normal life, including freedom of movement, access to labour markets, education and health services".
The UN children's agency, UNICEF, said 80 percent of the Rohingya refugees who had fled to Bangladesh were women and children.
In northern Rakhine state, UNICEF workers are unable to reach 28,000 children in need of care while work on clean water, sanitation and school repairs has been suspended, the aid agency said in a statement.
Myanmar says its security forces are fighting a legitimate campaign against "terrorists" responsible for a string of attacks on police posts and the army since last October.
Officials in the country blamed Rohingya attackers for the burning of homes and civilian deaths, but rights monitors and Rohingya fleeing to neighbouring Bangladesh say the Myanmar army is trying to force them out with a campaign of arson and killings.
Source: Al Jazeera and news agencies