The Asahi, a major newspaper, said 56 per cent of Japanese are in favour of dissolving parliament and holding general elections 'as soon as possible', according to a telephone poll of 1,069 people it conducted Tuesday and Wednesday.
Only 43 per cent supported quick elections in an Asahi poll taken just before Mr Fukuda abruptly said on Monday that he would step down after less than a year in office, and poll results show many feel Mr Fukuda was irresponsible in leaving his post so quickly.
The poll did not give a margin of error.
The ruling Liberal Democratic Party, which has been reluctant to call new elections, effectively picks the prime minister from within its ranks because it holds a majority in the powerful lower house of parliament.
The party has announced that it will choose a new leader on Sept 22, and parliament was expected to install their choice as prime minister after it reconvenes on Sept 24.
Speculation over which party members would enter the race began immediately after Mr Fukuda made his surprise announcement, and on Thursday several put their name forward.
But opposition in parliament to ruling party legislation is high, and government business has been in a deadlock for more than a year because the leading opposition group, the Democratic Party of Japan, is blocking most bills and calling for nationwide elections to test the public mandate.
Parliamentary elections must be held by next September at the latest.
But the Liberal Democrats, who have controlled Japan's government for most of the post-World War II period, are thought to be vulnerable after both Mr Fukuda and his predecessor, Mr Shinzo Abe, had little public support and quit less than a year into their terms. -- AP