Half seats of the upper house are up to grab every three years.
The coalition's expected victory would give Abe a mandate for his "Abenomics" policies and his decision to delay a consumption tax hike.
Abe declined to say how big the package might be.
Noriko Okada, a 66-year-old interior decorator, said she voted for a Japan Communist Party candidate to show her opposition to constitutional revision.
Japanese are voting in a nationwide election for the upper house that may cement Prime Minister Shinzo Abe's grip on power, as he forges ahead with policies to encourage exports and easy lending to keep a shaky economic growth going.
A police officer walks past Japan's ruling Liberal Democratic Party's (LDP) poster (2nd from right) for the July 10 Upper House election with the image of Shinzo Abe, Japan's Prime Minister and leader of the LDP, and other candidates' posters at the LDP headquarters in Tokyo, Japan, July 10. "I have two more years to my term [as LDP president] and this is a goal of the LDP, so I want to address it calmly", he told broadcaster NHK.
Kyodo News reported voter turnout of 54%, up slightly from 53% in the 2013 upper house election. The lowest voter turnout for a House of Councillors election was 44.52 percent in 1995.
Voters went to the polls at about 48,000 voting stations; most opened at 7 a.m. and closed at 8 p.m.
Abe set a win-or-lose line at 61 seats, or a majority of the 121 being contested, for the ruling camp.
Mr Abe's governing Liberal Democratic Party now has 116 seats in the 242-strong upper house and can also count on 20 seats for its junior coalition partner, the Komeito party.
The coalition and friendly parties also won the two-thirds "super majority" that could allow them to begin the process of revising Japan's postwar, pacifist constitution, some TV exit polls showed. "I don't expect much from the elections".
"Abenomics has never failed but is still half done", Abe told voters in Tokyo late Saturday, winding up his election campaign. As a result, there were a record 32 one-seat constituencies.
Tobias Harris, vice president and an Asia specialist with Teneo Intelligence in Washington, D.C., said Sunday's vote was a "solid victory, as expected", for Abe, but it does not guarantee that Abe will be able to assemble the full two-thirds majority - 162 seats - in the upper house necessary for changing the constitution.
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More than a dozen other people received gunshot or bomb shrapnel wounds, including two who were in critical condition, he said. He said the security forces were largely successful in limiting the damage of the attack, though two police officers had died.
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