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The king cautioned against "any attempt to expel Palestinians from any of the Palestinian lands or cause them to flee”, Jordan's official news agency Petra reported.
The king “affirmed that the crisis should not be moved to neighbouring countries and compound the refugee issue".
He called for the “opening [of] urgent humanitarian corridors”, as well as "protecting civilians, de-escalating, and ending the war on Gaza", Petra reported.
Mr Blinken, who arrived in Amman from Israel, said that he understood "as a Jew, as a husband and a father" the enormity of the Hamas attack.
After meeting King Abdullah, Mr Blinken met Mahmoud Abbas at the Palestinian president's residence in Amman.
Mr Abbas "affirmed ... the total refusal to uproot our people in Gaza", the Palestinian news agency Wafa reported.
Such a scenario would be akin to a second Palestinian "catastrophe", Mr Abbas said.
The Palestinians consider the 1948 creation of Israel and the upheaval it caused as their national Nakba, or catastrophe.
US State Department spokesman Matthew Miller said the US was talking with allies in the Middle East "to prevent the conflict from widening".
He said Mr Blinken told Mr Abbas that "Hamas does not stand for the Palestinian people’s legitimate right to dignity, freedom, justice and self-determination".
Late on Friday Mr Blinken will travel to Qatar, the Arab country that is the most well connected to Hamas after Iran.
Hamas, which is supported by Iran, took scores of hostages in its attack on Israel at the weekend, including American citizens.
Jordan has the longest borders with Israel.
A large proportion of the kingdom's population are of Palestinian origin, descendants of the refugees who fled Israel's creation in 1948 and its expansion in the 1967 Middle East war.
The latest war in Gaza poses a challenge to authorities in Amman, which seeks to maintain a strong alliance with the US and keep a 1994 peace treaty with Israel, while placating pro-Palestinian sentiment in the kingdom.