In a new expression of that snub, Abbas overlapped with Pence in Jordan from Saturday evening to midday Sunday, when the Palestinian leader flew to Brussels for a meeting with European Union foreign ministers.
Pence reaffirmed President Donald Trump's decision to name Jerusalem the capital of Israel and move the USA embassy from Tel Aviv to Jerusalem, while adding the United States is committed to achieving peace between the two sides.
Arab politicians were thrown out of the Israeli parliament for heckling U.S. vice-president Mike Pence at the start of a speech on Monday.
Netanyahu appeared more interested in talking with Pence on other issues, including Iran, Israel's main enemy.
During his address, Pence vowed that the U.S. would "never allow" the Tehran regime to possess nuclear weapons - a message meant not only to reassure Israeli leaders, but also Sunni Arab states across the Middle East concerned by President Barack Obama's efforts to reach out to Iran.
Pence addressed another key part of Trump's December speech in his Knesset speech, saying the United States would move its embassy to Jerusalem by next year. The Palestinians have ruled out such recognition, saying it would disadvantage Israel's Arab minority.
He's the highest ranking United States official to visit Israel since President Trump's recognition of Jerusalem as Israel's capital in December.
A general strike in east Jerusalem is planned for Tuesday.
The brief exchange was part of an exceptionally warm welcome for Mr Pence in Israel. Abbas left for an overseas visit before Pence arrived, according to the reports.
Pence told the king that Washington was committed to preserving the status quo of holy sites in Jerusalem.
Israel insists it has been the capital of the Jewish people for 3,000 years and the country's capital for 70 years. In both Arab capitals, Pence received criticism regarding Trump's Jerusalem announcement.
Last week Abbas denounced Trump's peace efforts as the "slap of the century" and accused Israel of ending the Oslo accords that underpin negotiations - which have been effectively frozen since 2014.
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