Public broadcaster NHK and several commercial networks said exit polls on Sunday indicated the Liberal Democrats had won more than 300 of the powerful house's 480 seats.
NHK predicted the LDP, which held 249 seats in the house when Koizumi dissolved it, would win 309 seats. TBS, another network, said the LDP would win 307 seats.
The main opposition party, the Democrats, was expected to win 104 seats, a devastating plunge from its previous standing of 175 seats, NHK said.
An official vote count won't be released until Monday morning.
Shinzo Abe, a senior LDP official, expressed cautious optimism even after the networks called the election in his party's favour.
Koizumi called the elections after
defections in his party
"We hope we will be able to get a majority," he said.
"But you can't tell until all the votes are counted." Abe said that even if it won a majority on its own, the LDP would continue to govern with its coalition partner, the Buddhist-backed New Komei Party.
The opposition, meanwhile, conceded the race was tough.
"It was more severe than what we had expected," Koichiro Genba, the Democratic Party's elections committee chief,
said of the exit poll results.
Voter turnout was high, at 50% by evening, up 2.65 points from 2003 election, in part because of a dramatic battle over Kiozumi's efforts to reform Japan's postal system, which includes banking and insurance schemes worth 330 trillion yen (US$3 trillion).
The voter turnout rate was considerably higher than in the last elections in 2003. Absentee ballots also hit a record 8.96 million, or more than 8 percent of Japan's 103.4 million eligible voters. The overall turnout rate in 2003 was 59.9%, the second lowest since 1947.
The opposition is calling for more
independence from the US
Koizumi, 63, called the elections after defections from within his party scuttled his reform bills in the upper house on 8 August.
Since then the bachelor prime minister, who sports a silvery mop-top and a passion for opera, has kept voters riveted by purging 37 anti-reform lawmakers from his party and drafting celebrity candidates, including a TV chef and an internet mogul, to run as "assassins" against them.
Postal service reform
In the runup to the elections, Koizumi's battle with the LDP defectors completely overshadowed the Democratic Party, which tried to get voter attention by proposing a pension reform blueprint and sniping at Koizumi's military relations with Japan's top ally, the United States.
Katsuya Okada, the 53-year-old leader of the Democrats, urged the country not to focus solely on postal service reform.
"I did all I could and must now await for the voters' judgment," Okada said after voting with his wife Sunday morning. "The voters' reaction has been very good. It has never been this good before. It is a historic day for the people of Japan."
Aside from pushing pension reform, the Democrats oppose Japan's dispatch of troops to support the US-led coalition in Iraq and criticize Koizumi's controversial visits to a Tokyo war shrine, which enrage neighbouring Asian countries that say the site glorifies Japan's militaristic past.
The Democrats have also called for the repositioning of US troops based in the southern Japanese prefecture of Okinawa.