Paul initially sought to add an amendment that would put the Afghanistan inspector general in charge of overseeing U.S. aid to Ukraine. But he later blocked the votes on the bill and amendment, instead wanting to include language in the legislation creating the inspector general oversight.
"My oath of office is to the U.S. Constitution, not to any foreign nation ... We cannot save Ukraine by dooming the U.S. economy," Paul said on the Senate floor.
The outlet said Paul's move will push the vote until at least next week as lawmakers are leaving Washington, D.C., for the week.
"I think they're going to have to go through the long way," Paul told The Hill.
CNN reported that senators largely agree to having oversight of the distribution of aid to Ukraine, but the change in the legislation could slow the process of getting the funding to Kyiv.
"The package is ready to go," Schumer said. "The vast majority of senators on both sides of the aisle want it. There's now only one thing holding us back. The junior senator from Kentucky is preventing swift passage of Ukraine aid because he wants to add at the last minute his changes directly into the bill. His change is strongly opposed by many members of both parties."
The House voted overwhelmingly in favor of the bill Tuesday, 368-57.
The package includes $6 billion in assistance for training, equipment, weapons and logistics support as well as $8.7 billion to replenish U.S. stocks of military equipment that President Joe Biden's administration has already sent.
More than $5 billion is included to alleviate global food insecurity, $3.9 billion for European Command operations, $900 million allotted to refugee support services for arrivals from Ukraine and nearly $14 billion for the State Department to aid Kyiv.
Darryl Coote contributed to this report.