Pence reiterated earlier in Israel that his country would move its embassy to Jerusalem before the end of 2019, and that the USA administration is in support of a two-state solution, urging the Palestinian leadership to return to the table of negotiations.
President Donald Trump last month recognised Jerusalem as the capital of Israel and said he would move the U.S. embassy there - dismaying Palestinians who claim the eastern part of the city.
The visit to Israel comes amid a boycott by Palestinian Authority officials, who want the eastern part of Jerusalem as their own capital and say Trump's move has disqualified the U.S. as a mediator.
"I've had the privilege over the years of standing here with hundreds of world leaders and welcome them, all of them, to Israel's capital, Jerusalem", said Netanyahu.
Since the inauguration of Donald Trump, the U.S. administration has questioned whether or not to withdraw from the Iran nuclear deal, a plan that stipulates the lifting of global sanctions against Tehran.
Pence confirmed several elements of US-Israel policy in his speech, which received a mixed response from the Israelis.
Ashrawi refuted U.S. claims that Pence's visit to the Middle East was meant to protect Middle Eastern Christians, explaining that the real objective of the visit is to assure Israel that it and the United States are in the same trench considering that Pence is a fundamentalist Evangelical Christian who interpret the Old Testament literally.
Mogherini was asked about the changing role of the U.S.in the Israeli-Palestinian peace process, and responded: "We have been engaged with our American friends through the Quartet [on the Middle East]".
Prime Minister Benjamin Netanyahu praised Pence upon his arrival in Israel following stops in Egypt and Jordan.
Mr Pence said the administration will advance its plan in the coming weeks and the embassy will open by the end of 2019.
Pence was not expected to meet with Palestinian officials during his trip.
Speaking at a joint press conference with Palestinian President Mahmoud Abbas, Federica Mogherini reiterated the EU's commitment to a two-state solution, with Jerusalem as the shared capital of both states - the State of Israel, and the State of Palestine. "Thanks to the president's leadership, the alliance between our two countries has never been stronger".
Meanwhile, PA President Mahmoud Abbas's Fatah party called for a general strike across "all Palestinian sectors" to protest USA policy on Pence's second day in the country on Tuesday.
Israel and the United States "are striving together to achieve a true peace, lasting peace, peace with all our neighbours, including the Palestinians", Netanyahu said.