Democratic presidential candidate Sen. Kirsten Gillibrand of New York rejected President Trump's offer to extend protections for some undocumented immigrants for three years, reiterating House Speaker Nancy Pelosi's view of the deal as a "non-starter."

The president on Saturday laid out what he said was an offer to end the government shutdown, now the longest in history. He offered to extend protections under the Deferred Action for Childhood Arrivals (DACA) program and for Temporary Protected Status (TPS) holders in exchange for funding for border security in a bid to end the government shutdown.

"He's the one who got rid of the DACA protections in the first place," Gillibrand, who announced a run for president last week, said on "Face the Nation" Sunday. Mr. Trump's offer is only a "temporary respite," she said, insisting DACA protections must be given to "all the Dreamers" and include a pathway to permanent citizenship.

Gillibrand said a three-year DACA deal "doesn't accomplish what we need to accomplish. I think it's cynical."

"I don't take him on his word on anything," Gillibrand said, responding to a tweet by Mr. Trump on Sunday morning offering "amnesty" as part of a "bigger deal." "If he really cares about this, he would open up the government, stop the 800,000 people who didn't get a paycheck last week — stop their suffering ... It just shows the callousness that is unacceptable."

The president's latest offer still contains his $5.7 billion demand for a border wall, which Democrats continue to reject.

Gillibrand, who is campaigning as a "young mom" who will "fight for other people's kids as hard as I fight for my own," implored the president during her "Face the Nation" interview to show more empathy for DACA recipients and asylum seekers. In the same vein, she defended her "Medicare for All" campaign proposal, saying it will allow people to get "high quality health care that is less expensive."

On foreign policy, Gillibrand said she is "grateful" for Mr. Trump's direct diplomatic talks with North Korean leader Kim Jong Un, saying she appreciates he is "focused on diplomacy and not on bombing North Korea."

"Diplomacy and engagement [are] the right approach," she said, though she declined to answer whether she would continue the talks with Kim if she became president. She called Mr. Trump's first talks with Kim "much more of a political stunt."