U.S. government was headed for a partial shutdown unless Trump and Congress cut a deal in their long-running battle over Trump's demand for a border wall.
Trump urged his fellow Republicans on Thursday to put aside misgivings over letting young "Dreamer" immigrants stay in the U.S.
Senators from both parties said they were encouraged on Thursday about the prospects for bipartisan immigration talks.
U.S. government shutdown fizzles out as Senate deal struck.
U.S. Senate Republican leader Mitch McConnell said on Sunday it would be "ridiculous" for a fight with Democrats over immigration issues.
The U.S. Senate narrowly approve a tax overhaul, moving Republicans and President Donald Trump a big step closer to their goal of slashing taxes for businesses.
The U.S. Senate candidate Roy Moore has resigned amid the Alabama Republican's efforts to combat allegations of sexual misconduct that have roiled his campaign.
Mitch McConnell clung to slim hopes on Tuesday that his party could still dismantle Obamacare, despite lacking adequate support for a repeal bill.
McConnell said he had spoken with Myanmar's Aung San Suu Kyi and that she said she was working to get aid to the Rohingya Muslim affected by violence.
Trump and Mitch McConnell remain united on many priorities and will hold previously scheduled meetings after the August recess.
U.S. stocks ended up on Tuesday, with each of the three major indexes posting their best one-day percentage gains in over a week.