"We told him that we were ready to collaborate with him and meet the Israeli PM (Benjamin Netanyahu) under his auspices to build peace," Mr Abbas told reporters during talks with German President Frank-Walter Steinmeier.
Mr Abbas met Mr Trump in Washington last week for their first face-to-face talks.
Mr Trump announced last week that his first foreign trip as president will include stops in Saudi Arabia, Israel and the Vatican — the spiritual centres of Islam, Judaism and Catholicism.
The stop in Israel is expected on May 22, though it has not been officially confirmed.
A senior Trump aide last week did not rule out the possibility of a presidential visit to the West Bank, but said that it was likely to be contingent on security and Mr Abbas taking concrete steps toward peace.
Mr Trump has been seeking ways to restart moribund Israeli-Palestinian peace efforts.
As he hosted Mr Abbas in Washington, Mr Trump confidently predicted that a peace agreement was within grasp, brushing aside the complexities of a decades-old conflict that has bedevilled successive US leaders.
Mr Abbas said Tuesday that "we told him again of our commitment to a peace based on justice, with international resolutions and the two-state solution as references."
Mr Trump has however sent mixed signals over the Israeli-Palestinian conflict. He backed away from the US commitment to the two-state solution — Israel and an independent Palestinian state side-by-side — when he met Mr Netanyahu in February.
He said he would support a single state if it led to peace, delighting Israeli right-wingers who want to see their country annex most of the occupied West Bank.
Mr Trump also vowed during his campaign to move the US embassy in Israel from Tel Aviv to the disputed city of Jerusalem, a prospect that alarmed Palestinians but which has been put on the back burner for now.
At the same time, he has urged Israel to hold back on settlement building in the West Bank, a longstanding concern of Palestinians and much of the world.
One of Mr Trump's top advisers, Jason Greenblatt, held wide-ranging talks with both Israelis and Palestinians during a visit in March.