(New throughout, adds Republican senators' quotes)
WASHINGTON, Jan 4 (Reuters) - Urgent negotiations aimed at shielding young, undocumented immigrants from deportation intensified on Thursday as Republican senators emerged from a meeting with President Donald Trump expressing confidence a deal could be struck this month.
As a follow up to the Republican-only talks on so-called "Dreamer" immigrants, Trump is inviting senators from both major parties to the White House next week. Some senators told reporters the aim was to hold the meeting on Tuesday.
"Next week the president is inviting a bipartisan group of senators to the White House to discuss the next steps on responsible immigration reform," White House spokeswoman Sarah Sanders told reporters.
For at least the past four months, Democratic and Republican senators have been meeting behind closed doors to try to fashion legislation that would protect at least 700,000 undocumented immigrants who were brought into the United States as children.
Many of these Dreamers are from Mexico and Central America and have spent most of their lives in the United States, attending school and participating in American society, despite their illegal status.
Trump put their fates in doubt in early September when he announced he was ending former President Barack Obama's Deferred Action for Childhood Arrivals program that allowed these youth to legally live and work in the United States temporarily.
Unless Congress and Trump can agree on a legislative replacement, these immigrants will be subject to deportation at the beginning of March. For many, their protections already have expired.
Senator Thom Tillis, one of a handful of Republican senators who met with Trump on Thursday, returned to Capitol Hill after the meeting and said it was possible a bill could hit the Senate floor later this month.
"I think so. I think if people get serious about it and start focusing and get in the room together...I think well see progress next week," Tillis told reporters.
Republican Senator James Lankford expressed hope that at next week's bipartisan meeting Trump will produce a document that specifically lays out his administration's demands for additional border security measures and other immigration law changes to accompany the new protections for Dreamers.
(Reporting by Steve Holland, Richard Cowan, Amanda Becker, Susan Cornwell and Jeff Mason; Editing by Andrew Hay)