Shinzo Abe says his party must "move forward and achieve results" following its landslide election victory.
The conservative Liberal Democratic Party won almost 300 seats and, with its coalition partner, looks set for a two-thirds majority in the lower house.
The governing Democratic Party suffered major losses in Sunday's polls, with leader Yoshihiko Noda stepping down.
China has urged the new government to take "practical steps" to deal with the East China Sea territorial dispute.
The two countries are currently embroiled in a row over islands in the area that both claim.
"We think the most pressing issue is that Japan must show sincerity and take practical steps to appropriately deal with the present situation and work hard to resolve the issue and improve relations between the two countries," said Chinese Foreign Ministry spokeswoman Hua Chunying.
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On course to be Japan's seventh PM in as many years, Mr Abe faces tough decisions on the economy as well as China.
He said his party understood its "heavy responsibility".
"Our victory this time does not mean trust in the Liberal Democratic Party has been completely restored," he told a news conference on Monday.
"Rather, it was a decision by the public that they should put an end to the political stagnation and confusion over the past three years, caused by the Democratic Party's misguided political leadership."
Official results are expected later in the day, but tallies by Japanese media organisations suggest that the LDP secured 294 seats.
Together with the New Komeito Party's 31 seats, a coalition would have a two-thirds majority in the 480-seat chamber, putting it in a position to override the upper house on stalled legislation.
The DPJ, meanwhile, saw its seats reduced from 230 to 57 in the lower house, Kyodo news agency reported, a result outgoing Prime Minister Yoshihiko Noda called "severe".
The Japan Restoration Party - a tie-up between the right-wing former Tokyo governor and Osaka mayor - secured 54 seats, projections showed.
'Shift to the right'
Shares rose early on Monday after the win by Mr Abe, who has promised more public spending and says he will implement measures directed at weakening the yen and fighting deflation.
The US congratulated Mr Abe, with President Barack Obama saying he looked forward to " working closely" with the new government.
Chinese media have warned that Japan's "rapid shift to the right" had neighbours worried.
"History has proven many times that a peaceful Japan is a boon to the region and the whole world, while a restless Japan will bring new disturbances to the world," a Xinhua news agency commentary said.
Mr Abe, seen as a foreign policy hawk who has called for Japan's pacifist constitution to be revised and patriotic sentiment nurtured, has advocated a strong stance in the dispute.
He told journalists on Monday that the islands were Japan's "inherent territory" and that there was "no room for negotiation on this point".
But he said "persistent dialogue" with China was needed. "We need to have wisdom not to turn political issues into economic issues," he said.
Parliament is expected to formally endorse Mr Abe as prime minister on 26 December.
The LDP enjoyed almost 50 years of unbroken rule until it was ousted by the DPJ in 2009.
Mr Abe served as Japanese prime minister between 2006 and 2007 but stepped down, citing ill health, as support for his administration plummeted.
The DPJ was elected on its promise to increase welfare spending and break ties between the bureaucracy and big business.
But its failure to deliver on the economy and response to the 11 March 2011 earthquake and tsunami lost it support.