By James Pomfret

HONG KONG, March 11 (Reuters) - Polling kicked off across Hong Kong in crucial by-elections on Sunday, with opposition democrats urging the city's 2.1 million eligible voters to cast "protest" ballots against perceived meddling from China's Communist Party rulers.

The by-elections will fill four legislative council seats once held by pro-democracy lawmakers who were ousted from public office after authorities deemed they'd failed to take valid oaths of office. Critics slammed the move as politically motivated to weaken the opposition.

Prior to Sunday's polls, several prominent democracy activists including Agnes Chow were barred from running, drawing some international criticism, including from the European Union.

The opposition has since been hobbled in the 70-member legislature, having lost its power to veto most legislation, with pro-establishment and pro-Beijing parties now dominating.

Some democrats in the city of 7.3 million say these polls are crucial to redress the injustice of the disqualifications, and to prevent the council becoming a rubber-stamp parliament, like the National People's Congress in Beijing.

"This is a protest vote, a war on public opinion and a de facto referendum. It will show if Hong Kong people agree or disagree with the disqualifications," said 21-year-old student democracy activist Joshua Wong as he voted on Sunday.

"Hong Kong's system no longer has checks and balances and the rule of law we knew of has already become rule by law."

Hong Kong's leader Carrie Lam voted at a school in the exclusive Peak district but declined to speak with reporters as a small group of protesters scuffled with police nearby.

A former Hong Kong leader, Tung Chee-Hwa, said the elections were important as Hong Kong was at a "critical juncture".

"The time for squabbling should be over," he said, calling on voters to back those who are "constructive, practical and truly want to serve Hong Kong."

Fifteen candidates are running for four seats, though the results are hard to predict amid a subdued mood with early voter turnout on the low side, according to government figures.

"(The disqualifications) were definitely wrong," said one voter, 60-year-old Cheng Siu-ngor. "I hope after this time, more young people can rise up."

The prospect of China's President Xi Jinping staying in office indefinitely following the proposed abolition of term limits, has also stoked some unease amongst critics, given Xi's relative tough line on the freewheeling Asian financial hub.

During a visit to Hong Kong last July, Xi warned Beijing won't tolerate any challenge to its authority.