In a carefully worded interview broadcast on ABC News on Sunday, Vice President Kamala Harris declined to provide details on how the Biden administration would respond if Israel invaded the city of Rafah in southern Gaza, if Congress continued to refuse to pass border-security legislation and if TikTok’s Chinese parent company refused to sell the service.

Ms. Harris reiterated the administration’s previously stated position that Prime Minister Benjamin Netanyahu of Israel should not order an invasion of Rafah, where more than a million people have sought refuge from Israel’s aerial bombardment and ground operations throughout the rest of Gaza.

“We have been clear in multiple conversations and in every way that any major military operation in Rafah would be a huge mistake,” she said. “Let me tell you something. I have studied the maps. There’s nowhere for those folks to go, and we’re looking at about 1.5 million people in Rafah who are there because they were told to go there, most of them.”

But she did not answer when the interviewer, Rachel Scott, asked whether there would be “consequences” if Israel invaded Rafah anyway. Ms. Scott noted that Mr. Netanyahu had shown no inclination to follow the advice of the United States.

“Well, we’re going to take it one step at a time, but we’ve been very clear in terms of our perspective on whether or not that should happen,” Ms. Harris said, adding, after Ms. Scott repeated the question, “I am ruling out nothing.”

Asked about TikTok — which, under legislation that passed the House this month and is awaiting a Senate vote, would be banned in the United States unless the service’s Chinese owner agreed to sell it — she said the administration did not want to ban it but simply had “national security concerns about the owner,” ByteDance.

“We have no intention to ban TikTok,” she said. “In fact, what it serves in terms of, it’s an income generator for many people, what it does in terms of allowing people to share information in a free way and a way that allows people to have discourse, is very important.”

But she did not say that Mr. Biden would veto the bill if it passed the Senate.

Turning to immigration, Ms. Scott showed a video of migrants clashing with Texas National Guard troops along the border in El Paso and asked whether that conveyed to Americans “that the border is secure.”

“We are very clear, and I think most Americans are clear, that we have a broken immigration system and we need to fix it,” Ms. Harris said, criticizing Senate Republicans for, in the face of pressure from former President Donald J. Trump, backing away from a bipartisan border-security deal that some of their members had negotiated.

“They’re refusing to put it up for a vote, and in large part because we know the former president would prefer to run on a problem instead of fix a problem,” she said.

Asked about the possibility of executive action, which Republicans in Congress are demanding, she indicated that it was an option on the table but said, “That does not absolve the fact that the real fix is going to be when Congress acts.”