1219 GMT January 21, 2018
Conservative premier Abe, 63, is facing an unexpected and fierce challenge from the media-savvy Koike, who has upended the sleepy world of Japanese politics with her upstart "Party of Hope", Reuters wrote.
Addressing hundreds of commuters at a busy Tokyo station via loudspeaker, Koike called on supporters to "end the politics of Abe," lashing out at the long-serving.
"The political status quo has continued while politics itself has lost the public's confidence," charged the former TV anchorwoman, 65.
Abe cut a contrasting figure by kicking off his offensive in the bucolic farming country of Fukushima, signaling his commitment to rebuilding the region hard hit by the 2011 nuclear power plant meltdown.
He pledged a major expansion of social programs, including offering free early-childhood education in a bid to get more women into work, while also talking tough on North Korea.
In an obvious dig at Koike, he urged voters to consider his policies, rather than catchy soundbites.
"Slogans do not open the way to the future. Policies unlock the future. We must not lose," he said.
The 12-day campaign will be fought around reviving Japan's once world-beating economy and the ever-present threat of North Korea which has threatened to "sink" the country into the sea.
Koike's "Party of Hope" has swallowed up and replaced most of the main opposition party in the space of a week, transforming Japan's staid political landscape.
But surveys suggest her bandwagon is grinding to a halt as she refuses to run herself for PM in the election, focusing on stewarding the world's most populous city with three years until Tokyo hosts the Olympic Games.
A poll in the top-selling Yomiuri daily suggested that 32 percent of voters plan to vote for Abe's conservative LDP with 13 percent for the Party of Hope — down six percentage points from the previous poll in late September.
On the streets of Tokyo, Abe's message that the election is about the coming generations appeared to resonate.
"At my age, what interests me is the future of my children and my grandchildren. We need to prepare a better world for them," said 76-year-old pensioner Sumiko Sakai.
Referendum on Abe
Abe is seeking a fresh term at the helm of the Asian economic powerhouse and key US regional ally and unexpectedly called a snap election to capitalize on a weak and fractured opposition.
But Koike stole his limelight by launching her party, attacking Abe's government for being too slow to reform the country, weighed down by an aging population, deflation and a huge debt mountain.
Abe's trademark "Abenomics" policy — a vow to kick deflation and achieve two-percent inflation with stable growth — has largely fallen flat.
Analysts say the October 22 vote is effectively a referendum on Abe, who has enjoyed unrivalled political strength for the past five years.
For her part, Koike says her new group promotes "compassionate conservatism" and hopes to distinguish herself from Abe by pledging a phase-out of nuclear power by 2030 and a freeze on a planned sales tax hike.
Koike sceptics charge that she repeats vague, catchy phrases and lacks details including how to pay for her ambitious projects.