The two world leaders held a phone conversation today - their first contact since Mr Trump’s inauguration six weeks ago.
Spokesman Nabil Abu Rdainah said after the call: "President Donald Trump invited President Abbas to visit the White House very soon.”
He said Mr Abbas was “convinced that President Trump is serious about achieving peace and is looking for a deal to achieve the long-awaited peace”. The last round of peace talks mediated by the US collapsed in 2014.
The invite signals an attempt by the Trump administration to improve relations with the Palestinians after a series of controversial statements on geopolitics in the region.
During a visit by Israeli Prime Minister Benjamin Netanyahu to Washington last month, Mr Trump suggested the US was no longer wedded to a two-state solution.
He has also stated his intention to move the US embassy from Tel Aviv to Jerusalem.
Despite the apparent change in tone, last week the Trump administration warned Israel against annexing parts of the occupied West Bank, saying it would trigger an "immediate crisis".
Earlier on Friday, Mr Abbas spoke to the US President about Israeli settlement building on occupied land and the need for a two-state solution to the conflict.
Mr Netanyahu and Mr Trump have spoken on the phone at least twice since the 20 January inauguration.