The result would shore up Abe's ruling coalition ahead of a tax hike later this year and keep alive the prime minister's plan to amend the country's pacifist constitution.
The 64-year-old Abe's Liberal Democratic Party and its coalition partner Komeito are forecast to take between 67 and 77 of the 124 seats -- about half the chamber -- up for election on Sunday, public broadcaster NHK said.
NHK's projection, based on exit polling and other analysis, came immediately after polls closed at 8:00 pm (1100 GMT).
The two parties control 70 seats in the half of the 245-seat chamber that is not being contested, putting them on track to maintain their overall majority.
Local media also predicted that forces in favour of revising the constitution, led by Abe's LDP, were set to win close to 85 of the seats up for grabs, giving them a "super majority" in the chamber.
Abe, who is on course to become Japan's longest-serving prime minister, was widely expected to maintain his majority, mostly due to a lacklustre opposition.
Pollsters had suggested turnout could be lower than 50 percent, significantly less than usual.
"I support the current government because I see no alternative," said Yoshiko Iida, a 45-year-old beauty therapist.
"Opposition parties are woeful," she told AFP. "I don't want to leave power to them."
Susumu Rokkaku, an 85-year-old male pensioner, said: "I voted for an opposition candidate but whoever is elected, nothing will change. I have no expectations."
"Abe's strength is largely based on passive support resulting from disarray in the opposition camp and a lack of rivals," Shinichi Nishikawa, professor of political science at Meiji University in Tokyo, told AFP.
If he wins, Abe should be able to stay in power until November when he will break the record of the nation's longest-serving premiership held by Taro Katsura, a revered politician who served three times between 1901 and 1913.
Abe's ruling coalition has sought during campaigning to win voter support for a rise in consumption tax to 10 percent later this year as part of efforts to ease swelling social security costs in the "ultra-aged" country.
He also hopes to secure a two-thirds majority in the upper house to keep alive his plans to amend the constitution's provisions on the military.
Abe vowed earlier this month to "clearly stipulate the role of the Self-Defence Forces in the constitution," which prohibits Japan from waging war and maintaining a military.
The provisions, imposed by the United States after World War II, are popular with the public at large, but reviled by nationalists like Abe, who see them as outdated and punitive.
"Since the ruling coalition is widely expected to win the election, attention is now focused on whether the pro-revision forces can win a two-thirds majority," Nishikawa said.
However, any constitutional revision also requires approval in a national referendum.