SOFIA, Nov 16 (Reuters) - Tens of thousands of opponents and supporters of Socialist-led government rallied on Saturday, underscoring the widening political divide and uncertainty in the European Union's poorest country.

Prime Minister Plamen Oresharski pledged to stay in power and push with reforms to help the most disadvantaged and raise incomes at a rally organised by the Socialists and their junior coalition partners, the ethnic Turkish MRF party in Sofia.

In a separate rally in Bulgaria's second largest city, Plovdiv, thousands of supporters of the main opposition GERB party demanded government's resignation and early election, accusing the government of incompetence and graft.

The Socialist-led cabinet took office in May after a GERB centre-right government resigned following mass protests over high utility bills and corruption. GERB won most votes at the May poll, but failed to form a government.

The cabinet enjoys a shaky majority with the unofficial support of nationalist Attack party. Most analysts say it will not carry out its full four-year term.

Many Bulgarians had hoped that joining the EU six years ago would bring prosperity to the former communist state and put an end to rampant corruption and organised crime. They are disillusioned with the entrenched political elites, which they believe work only for their own benefit.

The country is yet to put a senior government official behind bars for graft, while the average salary of 400 euros ($540) per month is the lowest in the 28-member bloc.

Five months after the early election, Bulgarians remain divided on whether the government should stay in power or resign, opinion polls show. Political analysts said Saturday's rallies can deepen the divisions.

"These demonstrations underscore the deepening confrontation between the political rivals. There is a possibility of intensification of the divisions in society," Parvan Simeonov, a political analyst with Gallup told private television Nova TV.