Israeli Prime Minister Benjamin Netanyahu's office responded, condemning what it called "the Jordanian government spokesman's support for the terrorist attack".
Palestinians were disappointed when Trump failed to mention a two-state solution with Abbas at the White House on May 3.
"My consistent and unequivocal position is that the U.S. Embassy should move to Jerusalem, as should other embassies", Netanyahu said at the meeting.
Israeli police said that a Palestinian man was shot dead after he stabbed and moderately injured a police officer in East Jerusalem's Old City on Saturday.
On Sunday, U.S. Secretary of State Rex Tillerson said Trump was considering the best move to facilitate renewing Israeli-Palestinian peace talks that have been frozen since 2014, hinting he might not make good on his election campaign promise.
The spat reportedly erupted during preparations for Trump's visit to the region next week.
Trump will arrive in Israel on May 22, when he will visit the Western Wall and meet with President Reuven Rivlin and Netanyahu.
A senior member of the US delegation for President Donald Trump's visit to Israel next week reportedly angered Israeli officials when he said the Western Wall was "part of the West Bank".
David Friedman, the newly minted USA ambassador to Israel who has long argued for recognizing Jerusalem as Israel's capital and was slated to begin living and working in Jerusalem from the start of his tenure, is expected to begin his post this week working out of the United States embassy in Tel Aviv, according to sources familiar with his plans.
The most recent waiver signed by President Barack Obama expires June 1. "The President is being very careful to understand how such a decision would impact a peace process", he said.
"Moving the American Embassy to Jerusalem would not only not harm the peace process, rather the opposite".
He said he will ask Modi tomorrow to use Indias "good offices" in bringing in peace between Israel and Palestine.
Jason Greenblatt, Trump's special representative on peace negotiations, led the US delegation of National Security Council and State Department officials in both Washington and overseas.
A wave of unrest that broke out in October 2015 has claimed the lives of 263 Palestinians, 41 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton, according to an AFP count.
Bennett said he was not sure why Trump has changed his rhetoric.