The cash-strapped Palestinian Authority, an interim self-government body set up following the 1993 Oslo peace accords, has suffered a series of financial blows in the past year.
Under interim peace deals, Israel collects taxes in the West Bank and in the Gaza Strip and makes monthly payments to the PA, which says it receives around $222 million each month.
The Finance Ministry said on Wednesday it collects about 700 million shekels ($193 million) in Palestinian taxes and transfers around 600 million shekels of that to the Palestinian Authority after deducting payments for electricity, water, sewage and medical treatment services.
On Sunday Israel said it would freeze about 5 percent of that against stipends the Palestinian Authority pays to families of Palestinians who committed terror acts against Israel.
In remarks made late on Tuesday and broadcast on Palestinian radio on Wednesday, Abbas said the PA would continue to pay out these stipends rather than accept a partial transfer of the tax revenues from Israel.
"We reject the tax, we don't want it," Abbas told visiting US congressmen. "Frankly, if we are left with only 20 or 30 million shekels, which is the sum paid to families of martyrs, then we will pay them to the families of martyrs," he said.
Israel and the United States say the stipend policy fans Palestinian violence while the Palestinians see the slain and jailed Palestinians as heroes of a national struggle.
The United States last year passed legislation to sharply reduce aid to the Palestinian Authority unless it stopped the pay-outs. The measure, known as the Taylor Force Act, was named after a 29-year-old American military veteran fatally stabbed by a Palestinian while visiting Israel in 2016.
Last month the Palestinians declined some $60 million in US annual funding for their security forces, worried about exposure to lawsuits under new US anti-terror laws.
Washington has further slashed hundreds of millions of dollars to humanitarian organizations and UN agencies which aid the Palestinians as it seeks to pressure Abbas to enter peace negotiations with Israel. Peace talks have been frozen since 2014.
The Palestinians suspended ties with Washington after President Donald Trump recognised Jerusalem as Israel's capital in 2017 and opened the new US Embassy in the city in May.
Israel has at times withheld the tax money over other matters.