He attributed the attack to Iran-backed militia groups.
They were the first US deaths in months of strikes against American forces across the Middle East by Iranian-backed militias amid the Israel-Hamas war in Gaza, increasing the risk of escalation.
Mr Biden said the United States “will hold all those responsible to account at a time and in a manner our choosing”.
Jordan is a kingdom bordering Iraq, Israel, the Palestinian territory of the West Bank, Saudi Arabia and Syria.
US troops have long used Jordan as a base. Some 3,000 American troops typically are stationed in Jordan.
Since Israel’s war on Hamas in the Gaza Strip began, US troops in Iraq and Syria have faced drone and missile attacks on their bases.
The attack on Jordan marks the first targeting of American troops in Jordan during the war.
Mr Biden was briefed on the attack on Sunday, White House press secretary Karine Jean-Pierre said.
Jordanian state television quoted Muhannad Mubaidin, a government spokesman, saying the attack happened outside the kingdom across the border in Syria.
The conflicting information could not be immediately reconciled.
Mr Biden, who was in Columbia, South Carolina, on Sunday, was briefed by defence secretary Lloyd Austin, national security adviser Jake Sullivan and principal deputy national security adviser Jon Finer, Ms Jean-Pierre said.
Syria is still in the midst of a civil war and has long been a launch pad for Iranian-backed forces there, including the Lebanese militia Hezbollah.
Iraq has multiple Iranian-backed Shiite militias operating there as well.
Jordan, a staunch western ally and a crucial power in Jerusalem for its oversight of holy sites there, is suspected of launching airstrikes in Syria to disrupt drug smugglers, including one that killed nine people earlier this month.
