(Reuters) - Loyalists of Azeri President Ilham Aliyev swept the board in a parliamentary election on Sunday that mainstream opposition and international monitors had shunned. Candidates from the ruling Yeni Azerbaijan (New Azerbaijan) Party won the majority of 125 seats in the single-chamber parliament, the Central Election Commission (CEC) head said early on Monday.

Parliament is elected every five years through voting for individual candidates in electoral districts.

CEC head Mazahir Panakhov read the list of winners after counting the results from all 125 districts, which indicated that the ruling party got at least 70 seats in the new parliament.

A host of small parties and "independents" loyal to the government took almost all the rest.

Sunday's victory further cements Aliyev's grip on this mainly Muslim country of about 9 million people between Iran, Russia and Turkey, cushioned against calls for reform by its strategic importance to the West as an oil and gas exporter.

Aliyev has consolidated his power since succeeding his father, long-serving leader Heydar Aliyev, in 2003. Ilham Aliyev has presided at a time when officials say revenues from rising oil and gas exports have delivered better living standards.

The ruling party claimed victory shortly after polls closed. Exit polls, conducted by local and foreign companies, also indicated a ruling party victory.

Rights groups have accused the government of curbing freedoms and silencing dissent, while the opposition has complained of harassment, a lack of access to broadcasting, and draconian restrictions on campaigning.

The government has denied wrongdoing. Western governments have balanced their criticism over human rights with strategic considerations.

Azerbaijan is host to oil majors including BP Plc, Exxon Mobil Corp and Chevron Corp.

The opposition has already cried foul over the election.

"The election in Azerbaijan is conducted in an undemocratic environment," the opposition Musavat Party's leader, Arif Gajily, told Reuters. "Our observers monitored a lot of violations, including ballot stuffing, during the vote."

Musavat and other mainstream opposition parties in Azerbaijan boycotted the poll.

Human Rights Watch said this week that Azeri authorities had convicted or imprisoned at least 35 journalists and rights and political activists in 2014 and that "the crackdown continued at a dizzying pace."

The Organisation for Security and Cooperation in Europe (OSCE) said it would not monitor the election because restrictions imposed on it by the authorities made credible monitoring impossible.

The Azeri president, who left his polling station without making any statement, said later on Sunday that the OSCE's decision not to monitor the poll "was not acceptable."

Some foreign journalists, including reporters from Reuters, were not given accreditation to cover the election. The foreign ministry cited technical difficulties.

(Reporting by Nailia Bagirova; Writing by Margarita Antidze; Editing by Jonathan Oatis)