He has threatened to take Israel to the International Criminal Court (ICC) unless the full amount is released.
Israel collects taxes on behalf of the Palestinian Authority (PA), but halted payments in January.
It had frozen transfers in protest at the Palestinians joining the ICC.
Palestinian membership began on 1 April, giving them the option to pursue Israel for alleged war crimes.
Israel says it has deducted the cost of services provided to the Palestinian population, including electricity, water and hospital bills.
The government made the decision to restart payments two weeks ago but warned at the time that it would make deductions from the transfer.
Israeli Prime Minister Benjamin Netanyahu said at the time the "deteriorating situation in the Middle East" and rise of extremists required him to "act responsibly".
Speaking at a rally in Ramallah, President Abbas demanded the tax revenues in full.
"We are returning the money. Either they give it to us in full or we go to arbitration or to the ICC. We will not accept anything else."
An official at Mr Netanyahu's office told Reuters they were "willing to transfer back to the Palestinian Authority the sum that was returned whenever it wishes".
The decision to freeze the tax transfers to the PA, which provide two-thirds of its income, forced it to cut by 40% the salaries of thousands of government employees and announce an emergency budget.
Israel has suspended the transfers on three occasions in the past decade, but in January the Palestinian economy was already struggling, with the deficit at around 15% of GDP, unemployment at 25%, output set to contract, and donors not fulfilling funding commitments.
This content was originally published by the BBC at the following address: http://www.bbc.com/news/world-middle-east-32193371