Friedman responded to Abbas's remarks at a conference on anti-Semitism in Jerusalem, adding "anti-Semitism or political discourse?"
In January, Abbas railed against the White House, cursing Trump, saying, "May God demolish your house".
"President Abbas's comments were outrageous and unhelpful", she said.
Netanyahu said Trump's decisions on Jerusalem appeared to have brought Abbas to the point of making a verbal attacks on a USA official. "The US administration wants the plan to be productive, and therefore will wait for calm - which, in the meantime, is nowhere in sight", the source added.
He said Mr Abbas's "response was to refer to me as a son of a dog".
Earlier in Twitter comments, Friedman suggested that the settlements were part of Israel, while also reproaching the Palestinian Authority for its unwillingness to condemn an attack in the West Bank that killed two Israeli soldiers.
The White House forcefully pushed back on Monday night against a fresh round of insults from Palestinian Authority President Mahmoud Abbas hurled at a senior member of the Trump administration, after remaining quiet for months through his attacks following their decision to recognize Jerusalem as Israel's capital. "Not for me to judge, I leave that all up to you".
He criticised the United States recognition of Jerusalem as Israel's capital, the American plan to move its embassy to the city and the cutting off of hundreds of millions of dollars in aid to the UN agency for Palestinian refugees. "For the first time in decades, the U.S. administration has stopped spoiling the Palestinian leaders and tells them 'enough is enough.' Apparently the shock of the truth has caused them to lose it".
China's Xi begins second term with stark warning to Taiwan
This is the aspiration of all Chinese people and this is also inline with the fundamental interests of the Chinese nation. Xi has a hardline approach to Taiwan, and experts believe he intends to reunify Taiwan with China in coming decades .
Relations have grown even worse since Hamdallah and Palestinian security chief Majid Faraj's convoy was attacked by a roadside bomb in the Hamas-controlled Gaza Strip on March 13.
The Islamist group that rules the Gaza Strip said Abbas' "irresponsible statements" sought to "bring our people in the Gaza Strip to their knees at this hard and risky phase".
The harsh criticism comes amid great tension between Hamas and the PA, which have failed to implement a reconciliation framework signed in October previous year aimed at ending a decade-long split between the rival Palestinian factions.
Fatah, the ruling party within the PA, and Hamas, the party that governs the occupied Gaza Strip, signed a reconciliation agreement in October 2017, ending a decade of division that saw two parallel governments operating in Gaza and the West Bank, respectively.
"Abbas is tampering with the process of justice and investigation", Hamas said.
Abbas has already withheld electricity payments to the coastal enclave in an attempt to pressure Hamas to cede power, causing blackouts for Gaza residents.
The blockade of the Gaza strip, which includes land, air and sea blockade by Israel and Egypt, began in 2007.