The US Senate and Congress in general are unlikely to pass new border security restrictions by the end of the year, which are crucial for the allocation of billions of dollars in aid to Ukraine, as discussions are underway behind closed doors.

"Negotiating Sens. James Lankford (R-Okla.), Kyrsten Sinema (I-Ariz.) and Chris Murphy (D-Conn.) met for three hours on Sunday and continued to cite forward progress afterward, with Sinema saying some portions of the challenging border language had been finalised," Politico has reported.

However, the full agreement is reportedly still not finalised to a sufficient level to allow even a cursory outline or summary to be presented. Republican senators have suggested that the bill should not be considered until January.

Lankford noted that waiting for a final vote until January was a "realistic timeline" for completing their efforts. He said senators are "working through this as fast as we possibly can."

Senators will resume discussions on Monday when the Senate returns to work. However, even with a final bill, it might still take a week or more for the Senate to approve it.

Senate negotiators have been meeting daily to reach an agreement on border security measures demanded by House and Senate Republicans as a condition for passing a US$106 billion supplemental aid package that includes support for Ukraine and Israel.

Any agreement in the Democratic-controlled Senate, which has a 51-vote majority, would also have to be approved by the Republican-controlled US House of Representatives.

The White House has urged Congress not to delay passing additional support for Ukraine, pointing to Russian President Vladimir Putin's new threats against Ukraine during his press conference on 14 December.