The human rights group, in a letter to China-friendly President Ma Ying-jeou, said Taiwan would set an example for Asia by doing away with the law and canceling pending sentences.
More than 70 percent of Taiwan's public backs the death penalty, though no executions have been carried out since 2005 and the issue is subject to lively debate.
Scrapping capital punishment could deal a new setback to the president, beset by domestic rows as his Nationalist Party (KMT) faces year-end local elections seen as a bellwether for the 2012 presidential race.
"We look to Taiwan as a leader in the region on progress toward abolition," Amnesty International interim Secretary General Claudio Cordone wrote.
"In a time of heightened political debate, we urge you to demonstrate leadership and continue on the path toward abolition." Justice Minister Wang Ching-feng quit last week after expressing opposition to the law under which about 500 inmates have been executed since 1987.
The death penalty, which in Taiwan is carried out by a bullet in the back or to the base of the neck, remains standard legislation around Asia, including Japan and China.
Amnesty International says about 7,000 death sentences were handed down in China in 2008 - the country with the highest execution numbers in the world - with 1,718 of the sentences actually carried out. China does not publicize most executions.
Former Taiwan president Chen Shui-bian, in office from 2000 to 2008, cut back on executions, leaving 44 inmates on death row since the last sentence was carried out in 2005.
Election losses for the KMT would chill Taiwan markets, which have firmed since Ma was elected in 2008 and began brokering new trade deals between the export-reliant island and economic powerhouse China, its political rival of 60 years.
Ma has a strong mandate as the KMT controls parliament and the presidency, but government ratings have dipped over its response to deadly Typhoon Morakot in August.
"Ma, as president, cannot avoid answering the letter, but he must be cautious when he replies," said Lin Hsin-yi, executive director of the Taiwan Alliance to End the Death Penalty.
