Abe's conservative Liberal Democratic Party (LDP) and its junior coalition partner Komeito are likely to win around 300 of 465 seats in the October 22 election, according to polls by Kyodo News and the Nikkei business daily.
Mass-circulation Yomiuri Shimbun said the LDP could secure a stable majority on its own, without needing its coalition partner.
A two-thirds majority in parliament would allow Abe to push through an amendment to Japan's pacifist constitution.
The hawkish premier has called for changes to the US-imposed law so it can turn its self-defence forces into a full-fledged army.
Support for Koike's newly founded Party of Hope, which has transformed Japan's political landscape and swallowed up the main opposition Democratic Party (DP), appears to be deflating, with surveys predicting it might win around 60 seats.
A new centre-left grouping of DP members that did not jump on the Tokyo governor's bandwagon could clinch 40 seats, according to the Yomiuri survey.
After an initial surge of support for Koike, critics say the Tokyo governor has suffered by not running herself in the election, meaning voters for her party are not sure who they are electing as PM.
The Asahi Shimbun daily said that Abe also appeared to be gaining from a divided opposition.
Abe is seeking a fresh term at the helm of the Asian economic powerhouse and key US ally and unexpectedly called a snap election to capitalise on a weak and fractured opposition.
But the media-savvy Koike stole his limelight by launching her party, attacking Abe's government for being too slow to reform the country, which is weighed down by an ageing 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.
Critics say Abe called the early election to divert attention from a string of scandals, including allegations of favouritism to a friend in a business deal -- which the premier strongly denies.
Before the campaign kicked off earlier this week, Abe's ruling bloc held a two-thirds majority, with his long-ruling LDP holding 287 seats and Komeito with 35.
Abe has said he would step down if his coalition fails to win a simple majority.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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