By Mohammad Nurul Islam and Wa Lone

COX'S BAZAR, Bangladesh/YANGON (Reuters) - Hundreds of Rohingya Muslims from Myanmar crossed the border to Bangladesh over the weekend and on Monday, aid workers said, seeking shelter from escalating violence in the northwest that has killed at least 86 people and displaced some 30,000.

An official from the International Organization for Migration (IOM), the United Nations' migration agency, who did not want to be identified, said he had witnessed more than 500 people enter its camps in the hills near the border on Monday.

Aid workers from other United Nations agencies and Reuters reporters in the IOM camps also reported seeing Rohingyas who said they had recently fled the fighting in Myanmar. The UN workers did not give specific numbers, but expressed concern about a sudden influx of people.

The bloodshed is the most serious since hundreds were killed in communal clashes in the western Myanmar state of Rakhine in 2012, and is posing the biggest test yet for the eight-month-old administration of Nobel Peace Prize winner Aung San Suu Kyi.

Soldiers have poured into the area along Myanmar's frontier with Bangladesh, responding to coordinated attacks on three border posts on Oct. 9 that killed nine police officers.

Moulavi Aziz Khan, 60, from a village in northern Rakhine, said he left Myanmar last week, after the military surrounded his home and set fire to it.

"At that time, I fled with my four daughters and three grandsons to a nearby hill ... later, we managed to cross the border," he said.

Myanmar's military and the government have rejected allegations by residents and rights groups that soldiers have raped Rohingya women, burnt houses and killed civilians during the military operation in Rakhine.

New York-based Human Rights Watch said at the weekend satellite images taken on Nov. 10, 17 and 18 showed 820 destroyed buildings in five villages in northern Rakhine, bringing the total number it says it has documented to 1,250.

CHECKING REPORTS

Myanmar's government has also rejected previous reports of Rohingya civilians trying to escape to Bangladesh.

Zaw Htay, presidential spokesman and member of the newly-formed information taskforce on Rakhine, said the government continued to investigate such reports, but had not so far been able to substantiate any of them.

"We checked with the military and police about people fleeing to Bangladesh since Oct. 9. Some people fled from their villages, but we put them back to their villages," he said.

"If something like that happened, we are concerned and we will continue to investigate. We are not rejecting all allegations...our government always checks all the allegations, and some were found to be untrue."

Myanmar's army has declared an "operations zone" in mainly Muslim northern Rakhine, where it says it is battling Islamist-inspired Rohingya insurgents, and it is not possible for international reporters to enter the area to verify claims.

Myanmar's 1.1 million Rohingya, viewed as illegal immigrants from Bangladesh by many of the country's majority Buddhists, are denied citizenship and face severe restrictions on their travel.

Up to 30,000 people are now estimated to be displaced and thousands more affected by the recent fighting, the UN has said.

Humanitarian operations that had been providing food, cash, and nutrition to more than 150,000 people have been suspended for more than 40 days.

The UN refugee agency called on the Myanmar government for access to allow it to distribute aid.

"The idea is to help them where they are, so that they wouldn't be forced to cross over into Bangladesh," Vivian Tan, regional public information officer for the United Nations High Commissioner for Refugees, told Reuters Television.

"If they can't get the assistance where they are then, if they are forced to cross into another country like Bangladesh, we're really appealing to the Bangladeshi government to honor its long tradition of hospitality and open its borders to these refugees."

(Additional reporting by Serajul Quadir in DHAKA and Juarawee Kittisilpa in BANGKOK; Editing by Alex Richardson)