Amending the Constitution requires the support of two-thirds of both houses of Parliament. Mr. Abeâs party and its allies had those numbers before Sundayâs elections, but the prime ministerâs political woes earlier this year, along with the publicâs 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.
âI think youâll see the conversation revolve all around what is doable,â said Sheila A. Smith, a Japan expert at the Council on Foreign Relations in Washington. âThe bargaining is what is interesting.â
Sundayâs 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 Japanâs 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.
âI would like to clearly say that this is a total defeat,â Ms. Koike said in comments to NHK.
Analysts said Mr. Abeâs victory did not represent an endorsement of his platform so much as a lack of strong alternatives.
âAbeâs reading was right that this was the right timing because the opposition was not ready,â said Ichiro Fujisaki, a former Japanese ambassador to Washington. âPeople have no other choices, really.â
Mr. Abeâs 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. Abeâs hawkish strategy toward North Korea than approved of it.
âThere is an Abe conundrum,â said Jeff Kingston, the director of Asian studies at Temple University in Tokyo. Mr. Abe is a candidate âwho is basically unpopular with voters, whose policies are not particularly popular, who doesnât get high marks for leadership, and yet he keeps winning in elections,â 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. Koikeâs 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.
In comments to NHK, Ms. Koike said she regretted her âchoice of wordsâ in excluding candidates from her party. âRather than an alternative, the party became a target of peopleâs criticism,â she said. NHK said that the Party of Hope won fewer seats than the Constitutional Democratic Party did.
Analysts said that since Japanâs 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 Japanâs postwar era.
âIf the rival parties of the L.D.P. are divided, the L.D.P. wins,â 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, âbasically people got confused.â
The election did little to change Japanâs 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 votersâ desire for stability.
Daniel C. Sneider, a lecturer in East Asian Studies at Stanford University, characterized Mr. Abeâs campaign message as an appeal to vague fears. âHe said, âThere is this bad threat thatâs out there, and you have to trust me because I know how to handle things,â â 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.
âThe L.D.P. has been serving such a long time and knows what to do,â Ms. Kobayashi said. âAnd I think Japan should become a country that can protect itself with amending the Constitution. Missiles have been flying over, but I donât think the U.S. will actually come to protect us.â
With the economy slowly improving, voters also seemed willing to accept Mr. Abeâs plan to raise a consumption tax that he has vowed to apply to child care and free university and college tuition.
âRight now, the world and Japanese economy have been recovering, which is good timing for Japan to increase the sales tax,â said Eiji Ikebe, 47, a human resources consultant who voted for the Liberal Democratic candidate in the Chofu neighborhood of Tokyo. âThe important thing,â he added, âis not to create too much confusion and turbulence in politics.â