Abe said voters supported the LDP to push his party's economic policies and said it would be the government's top priority.
"Now that we got rid of the twisted parliament, the LDP is going to face a test of whether we can push forward the economic policies so that the people can really feel the effect on their lives," Abe told NHK.
Japan's stagnant economy is showing signs of perking up, helped by the aggressive monetary and fiscal stimuli that Abe has implemented since he took office in late December. Stocks have surged, business confidence is improving and the weaker yen has eased pressure on vital exporters.
"I want them to carry on doing their best as the economy seems to be picking up," Naohisa Hayashi, a 35-year-old man who runs his own business, said after casting his ballot in Tokyo.
But long-term growth will depend on sweeping changes to boost competitiveness and help cope with Japan's rapidly graying population and soaring national debt. Such reforms, long overdue, are bound to prove difficult even with control of both chambers of parliament.
Abe also faces a decision this fall on whether to follow through on raising the sales tax next April from 5 per cent to 8 per cent, a move needed to shore up Japan's public finances, but one that many worry will derail the recovery.
Based on preliminary results collated by local media, the LDP and its coalition partner, New Komeito, won a combined 76 seats, giving them a total of 133 seats in the upper house, more than the 122 needed for a majority.
The LDP won 65 seats, which together with the 50 it held before the elections gives it 115, short of an outright majority.
The main opposition Democratic Party of Japan, which fell from power in December elections, lost nearly 27 seats.
Voter turnout was low, suggesting a lack of public enthusiasm. According to Kyodo News agency, 52 percent of eligible voters cast ballots, the third-lowest turnout since the end of World War II.
The Liberal Democrats' "Recover Japan" platform calls a strong economy, strategic diplomacy and unshakable national security under the Japan-US alliance, which allows for 50,000 American troops to be stationed in Japan.
The party also favours revising the country's pacifist constitution, drafted by the United States after World War II, to give Japan's military a larger role - a message that alarms the Chinese government but resonates with some Japanese voters troubled by territorial disputes with China and South Korea and widespread distrust of an increasingly assertive Beijing.
Abe has upset both neighbours by saying he hopes to revise a 1995 apology by Japan for its wartime aggression and questioning the extent to which Korean, Chinese and other Asian women were forced to provide sex for Japanese soldiers before and during World War II.
Revising the constitution would require two-thirds approval by both houses of parliament and a national referendum. Polls show the public is less interested in such matters than in reviving the economy and rebuilding areas of northeastern Japan devastated by the March 2011 earthquake and tsunami.
In his interview with NHK on Sunday night, Abe said he would not rush the debate on constitutional revision and seeks to "expand and deepen" discussion to gain public support over time. He said there was still some homework to do, including finalising details of a national referendum.
Abe also hinted at possibly cooperating with the new Restoration Party, co-led by outspoken Osaka Mayor Toru Hashimoto, in trying to reach the two-thirds majority. Hashimoto stirred up controversy in May when he said that Japan's wartime system of using Asian women in battlefront brothels was necessary at the time.
Chief Cabinet Secretary Yoshihide Suga said the LDP would try to make progress on constitutional revision because it's the party's long-cherished goal.
"We have sought to revise the constitution in order to have one of our own. We have finally come to a point where a revision is a realistic option. We would definitely want to deepen a discussion," Suga told broadcaster NTV.
- AP