The proposal emerged barely a week after House Speaker Mike Johnson, the top Republican in Congress, met with Senate party members and laid out his own plan to link Ukraine aid to Republican legislation known as "HR-2," which would restrict border access and set tight limits on asylum seekers.

No. 2 Senate Republican John Thune told reporters that Johnson's plan has "a lot" of support among Republicans in the Senate, adding: "It'd be strong."

Congress is facing a possible government shutdown when current funding for federal agencies expires on Nov. 17, and some House Republicans have called for adding border measures to any stopgap measure to keep government operations afloat.

The Republican-controlled House passed HR-2 in May, but the bill has gone nowhere in the Democratic-led Senate.

"These solutions, drawn from those found in HR-2, prioritize the concrete and significant policy reforms that are most critical to securing the border," said a one-page proposal released by Republican Senators Lindsey Graham, Tom Cotton and James Lankford.

Among other things, the Senate Republican proposal would resume construction of a border wall -- former President Donald Trump's signature goal -- in addition to deeming large numbers of migrants ineligible for asylum. It would also revive a controversial policy under which asylum seekers are told to remain in Mexico while their immigration case is heard.

Republican border provisions face broad opposition from Democrats in Congress and from President Joe Biden. Democrats control the Senate by a 51-49 margin, but the chamber's rules require 60 votes to advance most legislation, which gives Republicans leverage.

Despite similar opposition, Johnson passed legislation last week that offsets $14.3 billion in aid to Israel with previously allocated funds to the Internal Revenue Service.

He told reporters that a bill linking Ukraine aid to border security would come soon.

(Reporting by David Morgan; Editing by Scott Malone and Deepa Babington)