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7 year oldHis comments came after a UN General Assembly vote effectively repudiated Washington's controversial declaration.
A majority of countries backed a non-binding resolution affirming Jerusalem's status quo on Thursday.
Washington has for the past few months been drafting a new peace plan, though it has not divulged any details.
Donald Trump's controversial recognition of Jerusalem as Israel's capital two weeks ago was condemned across the Arab and Muslim world, and hailed in Israel.
As protests continued, a 24-year-old Palestinian in northern Gaza was killed in clashes with Israeli troops, the Palestinian health ministry said. Israel said it was looking into the report.
There were also violent confrontations between demonstrators and troops across the occupied West Bank for the third straight Friday, including in Bethlehem as the city, the traditional birthplace of Jesus, prepares for Christmas.
The Palestinian leader reiterated that he no longer accepted the US as a mediator in the peace process with Israel. He also rebuffed a new US framework for peace being developed by President Trump's Middle East envoy, Jared Kushner, before it has been launched.
"The United States has proven to be a dishonest mediator in the peace process and we will no longer accept any plan from the United States," Mr Abbas told a news conference in Paris.
While the details of the US plan are not known, it has been devised for months and there has been an expectation it will be publicly launched in early 2018.
The last round of US-brokered peace talks between Israel and the Palestinians collapsed amid acrimony in April 2014.
Mr Abbas has been emboldened by the outcome of the vote at the UN, which rejected any changes to the status of Jerusalem.
Thursday's vote came three days after the US used its power of veto to block a similar resolution at the world body's smaller, but more powerful, Security Council.
The US had warned countries not to support the latest resolution, threatening to cut off financial aid anyone who backed it.
However the resolution still passed with a decisive majority, as most nations, including Washington's allies, voted in its favour.
Washington perceives the diplomatic opposition to its position on Jerusalem as an attack on its own sovereignty.
It says it has the right to decide its own policies, including where it places its embassies. Alongside recognising Jerusalem as Israel's capital, Donald Trump ordered the US embassy to be relocated there from Tel Aviv, breaking rank with the rest of the global community which maintain their embassies in the coastal city.
While the US has been widely criticised for reversing decades of neutrality on the issue of Jerusalem, Washington says it is fulfilling an election pledge by Donald Trump to implement the Jerusalem Embassy Act passed by Congress in 1995 but continuously postponed.
The issue goes to the heart of Israel's conflict with the Palestinians and the wider Arab world.
The city is home to key religious sites sacred to Judaism, Islam and Christianity, especially in East Jerusalem.
Israel occupied East Jerusalem in the 1967 Middle East war. It annexed the sector in 1980, in a move not recognised internationally, and regards the whole of Jerusalem as its indivisible capital.
The Palestinians seek East Jerusalem as the capital of a future Palestinian state.
According to the 1993 Israel-Palestinian peace accords, its final status is meant to be discussed in the latter stages of talks.
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