Hours later, after a Senate agreement was reached to end the shutdown, Pence said alongside Israeli Prime Minister Benjamin Netanyahu that the impasse was ending "thanks to the firm stand taken by President Trump" and congressional Republicans.
Pence is set to deliver a speech to the Israeli Knesset, or parliament, later in the day.
"In the weeks ahead, our administration will advance its plan to open the U.S. Embassy in Jerusalem - and the embassy will open next year", Pence said.
The US move to recognize Jerusalem as Israel's capital broke with decades of worldwide consensus that the city's status should be settled as part of a two-state peace deal between Israel and the Palestinians.
Members of the main Arab party said earlier they would boycott Pence's appearance, referring to him as a "dangerous racist".
Palestinians seek East Jerusalem, including the walled Old City with its holy sites, as the capital of their own future state.
The Palestinians are furious at Trump's decision to recognize Jerusalem as Israel's capital.
Palestinian President Mahmoud Abbas has refused a meeting with Mr Pence.
Mr Abbas says America can no longer serve as mediator in Middle East peace talks. Such accords are usually only agreed with recognized states.
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The Palestinians are planning a general strike on Tuesday to protest Mr Trump's declaration.
A Palestinian walks over a poster of U.S. Vice-President Mike Pence during a protest against Pence's visit to Israel, in the West Bank city of Bethlehem on Sunday.
"I am here to convey a simple message from the hearts of the American people - America stands with Israel".
"The door's open. President Trump is absolutely committed to doing everything the United States can to achieve a peace agreement that brings an end to decades of conflict".
Pence said the USA would support a two-state solution, but only if both sides support it. Netanyahu's hard-line government is dominated by opponents to Palestinian statehood, making such a scenario unlikely.
"This was such an incredible, exciting, and important speech that Mike Pence just had in the Knesset", said Haskel.
"If there were any hopes for a breakthrough on a peace deal, I'd say that's pretty remote after the Jerusalem decision", said Makovsky, a member of the Obama administration's peace-negotiations team.
Pence told the parliament that Israel "can be confident" that the U.S will never compromise Israel's security.
Christians make up a small minority of the overwhelmingly Muslim Palestinian population in the West Bank, but relations between the two religious groups are typically cordial and tolerant - unlike in conflict-battered Iraq and Syria, where Islamic State extremists have persecuted Christians.
Israel will however enthusiastically welcome Pence, whose administration has pledged staunch support for the country.
"The Americans should understand that the Palestinians, the Arabs, everybody, will not accept an American plan that does not include Jerusalem, that does not include settlements, that does not include refugees", Malki said.