He urged the opposition to give its backing to a $17bn emergency economic package to help ease the pain of high energy and food prices.
The measures, unveiled last month, include support for the elderly and credit guarantees for small firms.
Currently the lower house of parliament is controlled by the ruling Liberal Democrat Party while the upper house is controlled by the main opposition Democratic Party and its smaller allies.
Although the upper house is less powerful, the opposition can still use its position to delay bills.
Earlier Aso appointed Kazuyoshi Kaneko to take on the post of transport minister following the resignation of the previous incumbent over a series of gaffes after only four days in the post.
The resignation of Nariaki Nakayama marked an embarrassing start for Aso's new government.
Nakayama had said on said on Saturday that Japan's liberal-leaning national teachers' union was "a cancer" and should be abolished.
Last week he had commented that Japan was "ethnically homogenous", drawing criticism from the Ainu, the indigenous people of northern Japan.
"The series of comments were extremely inappropriate and I apologise to the people and to those concerned," Aso said before reading his speech on Monday.
He was sworn into office as prime minister last Wednesday with the lowest public support of any newly-appointed prime minister in eight years.
Newspaper polls showed his approval rating at just below 50 per cent.
Nakayama, the outgoing transport minister, said he had decided to step to prevent the opposition from focusing on him instead of concentrating on emergency measures needed to shore up Japan's sagging economy.