Treasury Secretary Jacob Lew met with the Ukrainian prime minister on Thursday.
The senator was caught making the offer to the secretary of State on a live microphone.
The delay will make getting a bill done this week a heavy lift.
Some conservatives, including Senate hopefuls, rejected the popular bill.
The House could vote as soon as this week to help its government stand up to Russia.
The aid includes $1.1 billion in humanitarian assistance to address the fallout from the civil war in Syria and another $400 million to support an “anticipated transition” in the country and respond to “new contingencies” while promoting reforms across the region.
Federal health officials are partnering with 26 countries to prevent pandemics.
“The reforms to the Food for Peace program, which has fed billions of hungry people around the world over the last six decades, will increase the impact of this life-saving assistance,” said USAID Administrator Rajiv Shah.
The secretary of State's move brings the total U.S. contribution to more than $1.7 billion.
It restores $1.5 billion in annual aid that was partly suspended after military coup.