The report by the Xinhua News Agency didn't give any details of what Mr Hu, who it said spoke on Tuesday night in a speech to fellow Communist Party leaders, meant by the reference to elections or whether it might include allowing true opposition parties.
But China has been holding non-partisan elections to low-level village offices for a decade, and the party has long been rumoured to be preparing to hold competitive internal elections for its posts and to expand the so-called "village democracy".
Mr Hu called for "efforts to expand citizens' orderly participation in political affairs and guarantee the people's rights to carry out democratic election, decision making, management and supervision according to law", Xinhua said.
Mr Hu, who is the party's general secretary, also called for reforms to China's legal system and for government to be more responsive to the public, the report said.
The speech to Mr Hu's fellow members of the party's Politburo, the second-highest level of power, came on the eve of China's National Day the 54th anniversary of the day communist revolutionary Mao Zedong proclaimed the People's Republic of China.
Xinhua said its theme was "government by law and improving political ethics".
China's leaders allow four powerless, noncommunist parties to exist alongside the ruling party but have crushed efforts to set up a true opposition.
Mr Hu had been expected to unveil proposals for competitive elections to party posts in a July 1 speech on the anniversary of the party's founding.
But he surprised observers by making no policy proposals at all and devoting the speech to praising the policies of his predecessor, Jiang Zemin, who stepped down last year as party leader and retired this year as president.
The delay in publicly calling for reforms could reflect the difficulty that Mr Hu faces in establishing himself as China's leader following Mr Jiang's 13 years in power.
Mr Jiang still retains a post as leader of the commission that runs China's military, giving him continuing influence over government decisions.
He also succeeded in having many of his allies appointed to the party's ruling nine-member Standing Committee.
Mr Hu has tried to cultivate an image as a champion of ordinary people and has called for higher standards of professionalism and more responsiveness in government.
Mr Hu also called for "active and steady promotion of political system reform, expansion of socialist democracy and improvement of the socialist legal system", Xinhua said.
Mr Hu said all party and government policies must meet the needs of the people for economic and social development. He said the government should "quicken the pace of legislation and improve the quality of laws, and stick to administration by law and judicial justice", Xinhua said.