Amending the Constitution requires the support of two-thirds of both houses of Parliament. Mr. Abe’s party and its allies had those numbers before Sunday’s elections, but the prime minister’s political woes earlier this year, along with the public’s doubts about a constitutional change, created the possibility that he would lose the supermajority in the lower house.
Even with the votes he needs in Parliament, Mr. Abe now must persuade the public, as any constitutional change needs to be approved by a majority of voters. Polls have shown that voters are split on whether they would approve such a measure.
“I think you’ll see the conversation revolve all around what is doable,” said Sheila A. Smith, a Japan expert at the Council on Foreign Relations in Washington. “The bargaining is what is interesting.”
Sunday’s parliamentary victory could also embolden Mr. Abe to run next year for a third term as leader of the Liberal Democrats. If he won he would be Japan’s longest-serving prime minister.
But the results were a setback for Ms. Koike, who started her new party, Kibou no To, or Party of Hope, with great fanfare just hours before Mr. Abe called the early election last month. After she decided not to run for office, voters lost interest.
“I would like to clearly say that this is a total defeat,” Ms. Koike said in comments to NHK.
Analysts said Mr. Abe’s victory did not represent an endorsement of his platform so much as a lack of strong alternatives.
“Abe’s reading was right that this was the right timing because the opposition was not ready,” said Ichiro Fujisaki, a former Japanese ambassador to Washington. “People have no other choices, really.”
Mr. Abe’s public approval ratings dipped below 30 percent over the summer as he was dogged by a series of scandals, and opinion polls taken during the campaign found that more voters disapproved of Mr. Abe’s hawkish strategy toward North Korea than approved of it.
“There is an Abe conundrum,” said Jeff Kingston, the director of Asian studies at Temple University in Tokyo. Mr. Abe is a candidate “who is basically unpopular with voters, whose policies are not particularly popular, who doesn’t get high marks for leadership, and yet he keeps winning in elections,” Mr. Kingston said.
Ms. Koike, after starting her own party, probably helped Mr. Abe by setting off a further split in the opposition. The leading opposition Democratic Party initially offered to free all of its candidates to run under the banner of Ms. Koike’s party. But after she said she would submit candidates to a litmus test and require them to sign a loyalty pledge, the left wing of the Democrats split off and formed yet another new party, the Constitutional Democratic Party, which gained momentum during the campaign.
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In comments to NHK, Ms. Koike said she regretted her “choice of words” in excluding candidates from her party. “Rather than an alternative, the party became a target of people’s criticism,” she said. NHK said that the Party of Hope won fewer seats than the Constitutional Democratic Party did.
Analysts said that since Japan’s electoral system was based on awarding victories to candidates who get the most votes in a constituency, the proliferation of parties favored the incumbent Liberal Democrats, who have dominated Japanese politics for most of Japan’s postwar era.
“If the rival parties of the L.D.P. are divided, the L.D.P. wins,” said Koichi Nakano, a political-science professor at Sophia University in Tokyo. With two new parties forming just weeks before the election, Professor Nakano said, “basically people got confused.”
The election did little to change Japan’s record as one of the worst in the world for female political representation. Fewer than one in five candidates for the lower house were women, and projections early Monday morning showed that about one in 10 of the winners were women.
At a time when North Korean missiles have been flying over Japan and some here worry about the unpredictability of the United States under President Trump, Mr. Abe capitalized on voters’ desire for stability.
Daniel C. Sneider, a lecturer in East Asian Studies at Stanford University, characterized Mr. Abe’s campaign message as an appeal to vague fears. “He said, ‘There is this bad threat that’s out there, and you have to trust me because I know how to handle things,’ ” Mr. Sneider said.
That message resonated with voters like Natsuyo Kobayashi, 38, a caregiver at a center for the disabled who cast a vote for the Liberal Democratic candidate in Sayama, a suburban town outside Tokyo.
“The L.D.P. has been serving such a long time and knows what to do,” Ms. Kobayashi said. “And I think Japan should become a country that can protect itself with amending the Constitution. Missiles have been flying over, but I don’t think the U.S. will actually come to protect us.”
With the economy slowly improving, voters also seemed willing to accept Mr. Abe’s plan to raise a consumption tax that he has vowed to apply to child care and free university and college tuition.
“Right now, the world and Japanese economy have been recovering, which is good timing for Japan to increase the sales tax,” said Eiji Ikebe, 47, a human resources consultant who voted for the Liberal Democratic candidate in the Chofu neighborhood of Tokyo. “The important thing,” he added, “is not to create too much confusion and turbulence in politics.”