Remington Arms 'Lee Sporter'.

The one piece stock design as opposed to the Brit Lee-Enfield 2 piece. The frame, bolt and components are different on the Rem than the British Lee's.

The Remington was orig made as a Military rifle and the US did buy some.
The US was in the transition period looking for a repeater to replace the Trapdoor and this was one of the offerings at the time.
The version was the normal full stocked military rifle of the day. Some also sold to States for Militia primarily.
45-70 cal for US issue, but some of the Militia rifles were in 30-40K

The Rem Lee sporter version came about around 1910 +/-.
They came in a long list of calibers. The above plus calibers like 30WCF, 32-40, 35Win(?).

The sporters came in standard like the one shown and a Deluxe with better wood, checkering and the PG was slightly tighter design.
A grip cap and some other goodies were standard or available on the Deluxe.

The Rem-Lee sporters don't quite bring the same as a Lee/Speed Brit sporter. But an orig condition (the one shown is restocked) in Deluxe form will give them a run.

My Rem Lee sporter is a project rifle right now. I have 3 of the Lee/Speed sporters and they are beautiful rifles to handle and shoot.
Mine are all 303brit cal but they came in 4 or 5 other calibers as well. Lots of variations and options.