The bill, which would pardon people, including political leaders, was passed unopposed by the lower House of Representatives last week.
The Senate, whose final version of the bill could become law, will debate the bill starting next week, the Bangkok Post reported.
"I would like the Senate, which comprises elected and selected senators and those who are for and against the government, to exercise their judgment," Yingluck said during a televised speech at Government House.
Members of Parliament in the lower house should respect the Senate's decision, she said.
Those covered by the amnesty would include former Prime Minister Thaksin Shinawatra -- Yingluck's older brother -- who was toppled in the bloodless coup and who later was convicted of financial corruption while in office.
Thaksin, who led the Pheu Thai party in government, denied the allegations, but was sentenced in 2008 and soon after fled the country. He lives in Dubai from where his critics say he wields political power through his sister, who now leads the Pheu Thai party.
The amnesty likely would include Thaksin's sentence for corruption, the Post reported.
"The amnesty bill is a way out ... one of the ways that we should all consider if we all learn to forgive one another," she said.
"Since this government took power it has focused on reconciliation ... an amnesty isn't about forgetting our painful lessons, but about learning so it doesn't happen again to our young generation."
The bill was passed in the lower house unopposed, but in the absence of the main opposition Democrat Party, the Post report said.
Tensions have been rising in the past several weeks between police and protesters who have gathered in the streets to denounce the bill and the government's amendment extended an amnesty to cover political leaders.
More than 10,000 protesters -- many of them the government's Red Shirt supporters -- took to the streets of Bangkok on Monday to condemn the bill.
Red Shirts want justice for the killing of more than 90 of their fellow protesters on the streets of Bangkok in 2010. About 2,000 people were believed injured during the fighting when protesters blocked Bangkok's central old town streets for several weeks.
Yingluck hit out at the bill's detractors, saying they weren't ready for forgiveness and accused them of considering violence to defeat the government and destroy democracy, the Post said.
"I don't want the amnesty bill to be used as a political tool to stir debate by confusing the details and distorting it,'' she said.
The Post also reported that former Prime Minister Abhisit Vejjajiva, leader of the Democrat Party, continues to denounce the proposed legislation despite that, if passed, it would afford him amnesty.
The Department of Special Investigation and the Office of the Attorney General announced last week they would indict Abhisit and his former deputy prime minister, Suthep Thaugsuban, for alleged murder and attempted murder for their roles during the 2010 demonstrations.
Abhisit, who lost to Yingluck in the election of July 2011, said Yingluck wanted to roll back her brother's prison sentence for corruption to pave the way for his return to Thailand.
"The prime minister must come out of the shadow of her brother and the other people around her,'' Abhisit said.
Many Red Shirts would welcome the return of Thaksin, but abhor an amnesty for Abhisit who stands of accused of involvement in the put-down of the 2010 demonstrations.