Senate Homeland Security Committee chairman Ron Johnson warned Sunday about being “snookered again” by North Korea after the White House agreed last week to denuclearization talks with leader Kim Jong-un.

Citing previous deals that saw the United States give up more than it got, Mr. Johnson urged the administration to maintain its maximum-pressure policy on North Korea.

“Again, you have that history. Let’s not be snookered again,” said Mr. Johnson on CNN’s “State of the Union.” “Let’s not be Charlie Brown to North Korea’s Lucy. We’ve seen this movie before; that’s why we’ve called on President Trump to make sure that we maintain the maximum-pressure campaign.”

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The Wisconsin Republican added that, “If anything, I would continue to ratchet up sanctions until they again have complete, verifiable and irreversible denuclearization.”

Sen. Elizabeth Warren, Massachusetts Democrat, said she supported the “diplomatic approach” but worried Mr. Trump would be “taken advantage of.”

“Here’s what I’m concerned about: I want the president to succeed,” said Ms. Warren. “When the president succeeds in negotiations like this, the United States succeeds, it makes us safer, it makes whole world safer, but I am very worried he’s going to go into these negotiations and be taken advantage of.”

She cited concerns about staffing at the State Department, saying it had been “decimated.”

“There are a lot of issues involved with them and our State Dept has just been decimated,” said Ms. Warren. “We don’t have an ambassador to South Korea. We don’t have an assistant secretary for the entire region. There are all kinds of spaces that are open at the State Department generally and particularly in this region, and that matters when you’re going into negotiations like this.”

White House spokesman Raj Shah offered few details Sunday about the logistics of the summit, adding that “nothing’s been ruled out.”

“It’s going to be a time and a place to be decided. We don’t have an announcement right now but we have accepted this offer and we hope that it can be part of an important breakthrough,” Mr. Shah told ABC’s “This Week.”

Would Mr. Trump go to North Korea? “I don’t think that’s highly likely, but again, I’m not going to rule anything out,” Mr. Shah said.