"The vice president's meetings with the leaders of Egypt, Jordan and Israel are integral to America's national security and diplomatic objectives, therefore the vice president will travel to the Middle East as scheduled," said Alyssa Farah, Pence's press secretary.
In the hours leading up to his international departure, Pence had been having conversations with members of Congress to avoid a shutdown, one source tells CNN.
Pence, a former congressman who has helped lead Capitol Hill outreach for the White House, worked the phones on Thursday, calling GOP members about federal government funding and the potential shutdown.
The vice president is already taking his Middle East swing later than originally scheduled, after he delayed the visit to remain in Washington last month for the Senate tax vote
Pence travels to the Middle East amid heightened tensions in the region following President Donald Trump's
recognition last month of Jerusalem as Israel's capital
. The vice president is expecting to be be faced with many questions about the decision, particularly while visiting Egypt and Jordan, both of whose leaders have been critical of Trump's decision.
A senior White House official said they are expecting the issue to come up, adding, "We are prepared for that topic."
"The main theme for the vice president is going to be looking forward," the official said. "And how can all of the parties work together at this juncture and try to find out the best path forward for peace between Israelis and Palestinians."
While in the Middle East, Pence will not meet with any officials from the Palestinian territories. Palestinian Authority President Mahmoud Abbas canceled his scheduled meeting in December with Pence in the wake of the Jerusalem announcement.
In Egypt and Jordan, the vice president will hold bilateral meetings with the leaders of both countries, President Abdel Fattah al-Sisi and King Abdullah II, where counterterrorism discussions will be at the top of the agenda as well as the situation in Syria.
In Israel, the vice president will meet with Prime Minister Benjamin Netanyahu and President Reuven Rivlin, and will spend the second day of his trip in Israel visiting holy sites including the Western Wall and Holocaust Memorial Yad Vashem.
Pence will also deliver remarks to Israeli's parliament, or Knesset, where he would "take (the) opportunity to highlight the fact that he's speaking in Jerusalem the Capital of Israel," officials say.
In his speech to the Knesset, as well as in his discussions with Israeli leaders, Pence is expected to speak at length about Iran and its influence in the region and around the world.
"It's an opportunity to sit down with our most cherished ally in the region to represent the President and to sit down and talk not only about regional stability but also about the US-Israeli relationship with an eye of countering Iranian malign influence and security in the form of Iranian proxies and how we can both work together to help mitigate that threat," a senior White House official said.
In all these countries, Pence will also highlight his work with the US Agency for International Development, focused on relief efforts for persecuted religious minorities.
Last October, Pence announced that the Trump administration will no longer fund "ineffective" programs run by the United Nations to help persecuted communities and will instead send money to such groups directly through USAID.
Senior White House officials stressed the importance of the program to the vice president and added that Pence will raise the issue at each stop.