In an address to Palestinian officials, Abbas condemned Ambassador David Friedman's close ties with the West Bank settler movement, describing him as a "son of a dog".
The White House later on Monday slammed Abbas's "insults", saying he must choose between hate and peace.
Despite that, Greenblatt said that Washington would still press ahead with a peace plan.
Relations between Abbas's government and Trump's administration have broken down since the White House recognised Jerusalem as Israel's capital in December.
Palestinians also see the city as their capital and Trump's recognition broke with decades of U.S. policy that Jerusalem's status would be negotiated between the parties. Abbas used the point on settlements, which the PA views as illegal, as a segway to attack Friedman.
Palestinian Authority President Mahmoud Abbas does not intend to follow through on threats to levy new sanctions on the Gaza Strip, despite a barrage of threats made during his fiery speech on Monday, a Fatah source told i24NEWS. "He and his family bought homes in these occupied settlements, he is the son of a dog", Abbas said. Anti-Semitism or political discourse? "I'll leave that all up to you".
Mr Abbas has already taken steps to put pressure on Hamas, including reducing electricity supplies to Gaza and cutting the salaries of former civil servants.
Rahul should first apologise for misdeeds of Cong: Javadekar
Gandhi has asserted that the country was "fatigued" and only his party could show the way forward. Whereas, he said, "under the BJP's rule, the economy is moving at the pace of a tortoise".
"Such brutality and no condemnation from the PA!" he tweeted, referring to a Friday vehicle ramming that killed two soldiers and a Sunday stabbing in Jerusalem that left an Israeli dead, both carried out by Palestinians.
Israeli Prime Minister Benjamin Netanyahu also responded to Abbas' remarks. "They are shocked and because they are in shock, they're losing their temper and the truth is coming to light: they aren't interested in negotiations and they're refusing to achieve peace".
Israel has militarily occupied the West Bank and east Jerusalem since 1967. "He is reinforcing the plans to separate the West Bank from the Gaza Strip". He is a settler, and his family are settlers, and he is the USA ambassador in Tel Aviv.
At the same time, Abbas accused Hamas of carrying out the assassination attempt against PA Prime Minister Rami Hamdallah in Gaza last Tuesday.
Abbas said Hamas would have to give up control of Gaza or risk taking full responsibility for the enclave and its two million residents without any help from his Western-backed Palestinian Authority. Hamdallah and Palestinian security chief Majid Faraj were uninjured when a roadside bomb exploded as they entered the Gaza Strip, Reuters reported.
Six of his guards were lightly hurt.