Half of the upper house seats are being contested in the 29 July polls.
Mr Abe's ruling coalition currently controls the house, but his popularity waned after he took power last year.
Defeat would not automatically cost Mr Abe his job, as it is the lower house which chooses the prime minister, but he may feel compelled to leave.
Campaigning in Tokyo, Mr Abe acknowledged that he and the ruling Liberal Democratic Party would be fighting "a very tough battle" in the polls.
But he urged voters to stick with him. "It is important that you give me the power to carry out reforms," he said.
The BBC's Chris Hogg, in Tokyo, says that Mr Abe knows he has a fight on his hands.
In a recent poll, his popularity fell to 30%, and he has been hit by successive ministerial scandals.
Earlier this month his defence minister, Fumio Kyuma, resigned over comments he made about the atomic bombings of Hiroshima and Nagasaki.
A scandal-hit farm minister committed suicide in May and his successor is under scrutiny over his expense claims.
In January, Health Minister Hakuo Yanagisawa drew strong criticism after referring to women as "birth-giving machines".
But most damaging to Mr Abe has been the revelation that over the years the government has lost pension records affecting about 50 million claims.
Mr Abe has pledged to shake up the Social Insurance Agency, the department responsible for the mistakes, and to sort out the mess by early next year, our correspondent says.
But it is not yet clear whether that would be enough to reassure angry voters.
The ruling coalition has a majority in the lower house ,and defeat in upper house polls would not directly threaten the government.
But, analysts say, it would be an embarrassment to Mr Abe and one that could force him from office.
Güncelleme Tarihi: 12 Temmuz 2007, 14:09