Pence said they deserved their pay and benefits and service members and their families "shouldn't have to worry about getting paid."
"Despite bipartisan support for a budget resolution, a minority in the Senate has decided to play politics with military pay," Pence said at the base, speaking in front of a large US flag and a line of soldiers dressed in military fatigues.
The vice president spoke as Democrats and Republicans in Congress showed little indication of progress on negotiations to end the government shutdown in a feud over immigration and spending.
While Pence did not identify the culprits by party affiliation, Republicans argue that Democrats are blocking additional funding for the Pentagon by keeping the government closed. The shutdown means uniformed service members are currently working without pay.
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Pence said the Trump administration would "demand that they reopen the government" and will not reopen negotiations "on illegal immigration" until Congress reopens the government and they give soldiers and their families "the benefits and wages you've earned."
Landing aboard a C-17 military aircraft, Pence visited the undisclosed military base in the Middle East following his meetings in Amman with Jordan's King Abdullah II.
Journalists covering the vice president were asked to withhold the name and location of the base, and the number of troops stationed here, because of security and diplomatic concerns.
The 332nd Air Expeditionary Wing is stationed at the base and has dropped nearly half of the munitions during the operation to destroy the Islamic State group in Iraq and Syria. Pence credited the troops' "heroic actions" to dismantle terror organizations in the region.