BANGKOK (Reuters) - Thai junta chief Prayuth Chan-ocha and opposition supporters of ousted populist premier Thaksin Shinawatra both reached out to the United Nations on Monday as tension rises ahead of an August referendum on a new constitution.

Prayuth said he telephoned U.N. Secretary-General Ban Ki-moon to express concern about an upsurge in political pressure, just a day after police shut down an electoral monitoring center at the Bangkok headquarters of the "red shirt" anti-government movement, formally known as the United Front for Democracy Against Dictatorship.

"This morning I telephoned (Ban) to let him know about a movement of people who wish ill on Thailand," Prayuth told reporters.

"The junta will deal with people who are acting illegally."

Twenty-nine other electoral monitoring centers have been shut in recent weeks as Thailand prepares to vote on the constitution that critics fear will entrench the military's influence.

The red shirts say the centers are needed to prevent fraud. Red shirt leader Jatuporn Prompan said his group went to the regional U.N. headquarters in Bangkok on Monday.

"We would like the United Nations to come in and monitor," Jatuporn told reporters.

Thailand came under fire last month at a U.N. review of its rights record with some member states expressing concern over the deteriorating rights situation since the military took power.

Under the proposed charter, a junta-appointed Senate with seats reserved for military commanders would check the powers of elected lawmakers for a five-year transitional period.

The referendum will be the first real rest of the junta's popularity since it took power in a May 2014 coup.

The army toppled the populist government of Prime Minister Yingluck Shinawatra in another chapter in a decade of confrontation between the establishment and Yingluck's brother, Thaksin, and his red-shirted supporters.

(Reporting by Aukkarapon Niyomat and Panarat Thepgumpanat; Writing by Amy Sawitta Lefevre; Editing by Nick Macfie)