Representative Hakeem Jeffries, Democrat of New York and the minority leader, was forced to defend himself on Monday for taking a recent meeting with Jared Kushner, President Trump’s son-in-law and top outside adviser, amid a backlash about the encounter from some progressives.

“I wanted to give you a little real talk on this Jared Kushner situation,” Mr. Jeffries said in a video he posted on social media, in which he appeared in Brooklyn dressed in a bright green Yankees cap and matching polo shirt.

Mr. Jeffries, who had initially declined to acknowledge the meeting or comment on it, said in the video that Mr. Kushner had asked for the meeting, and he had taken it, in order “to discuss the affordability crisis that exists, that is not a hoax.” (Mr. Trump has accused Democrats of inventing the concept of “affordability” to attack him over the high cost of living.)

The discussion came as Mr. Trump and Democrats are attacking one another relentlessly on the campaign trail as they battle for control of Congress, and as the president’s inner circle is facing the increasingly likely possibility of a Democratic takeover, one that would put the Brooklyn lawmaker in line to be the House speaker.

It drew bitter criticism from some Democrats, who are eager to see accountability for the Trump administration on a range of topics after a pliant two years of House Republican control. They said his decision to privately huddle with Mr. Kushner raised questions about how tough Mr. Jeffries would be in investigating the administration.

“You do not meet with them — don’t have anything to do with them,” James Carville, the veteran Democratic strategist, vented online in a four-minute rant about Mr. Jeffries. “Any business we have is going to be conducted with you under oath.”

Mr. Jeffries insisted in the video that he would be aggressive.

“I shouldn’t have to say it, but I am,” he said. “No one is going to get a pass. We’re going to hold every single member of the Trump cartel accountable.”

A spokeswoman for Mr. Kushner did not respond to an email seeking comment on Mr. Jeffries’s video.

The confab, which was first reported by The New York Times on Sunday, was described by people familiar with it as a general get-together in New York City to discuss areas where the Trump administration and Democrats could find common ground, discussing housing, cost-of-living and immigration. Mr. Kushner used the discussion to suggest that Mr. Jeffries meet with Susie Wiles, the White House chief of staff, with whom the Democratic leader has no relationship, according to one of the people with knowledge of the meeting.

Mr. Kushner worked with Mr. Jeffries on criminal justice legislation during Mr. Trump’s first term, when he was an official senior adviser in the White House. Mr. Kushner now runs an investment firm backed heavily by Middle Eastern sovereign wealth funds and is not formally a part of the administration.

But he has been an increasingly key outside adviser to his father-in-law, playing a central role in aspects of Mr. Trump’s foreign policy since last summer, a fact that Democrats on the House Judiciary Committee have begun to investigate.

One of the most prominent faces of the Democratic left, Mayor Zohran Mamdani of New York, said he would still support Mr. Jeffries to lead the party. But elsewhere, there was outrage.

Mehdi Hasan, the founder of the news site Zeteo, called the meeting “pathetic stuff from the House Dem leader” in a social media post. Adam Kinzinger, the former Republican congressman who has been among Mr. Trump’s harshest critics, referred to the meeting by posting: “Make this make sense.”

Mr. Jeffries was already facing a potential rift within his caucus next year, with an incoming faction of anti-establishment members on the left who have repudiated him and broken with mainstream Democrats on a number of issues.

A person with knowledge of the meeting, who spoke on the condition of anonymity to discuss a sensitive topic, said it was a mutual friend, not the president’s son-in-law, who suggested that Mr. Jeffries and Mr. Kushner meet.

The meeting also created an awkward situation for Speaker Mike Johnson, Republican of Louisiana, who has been confidently predicting that his party will retain its majority and found himself pushing back on the idea that the Trump administration was instead preparing for a Democratic victory.

Asked on Sunday about the meeting, Mr. Johnson played down Mr. Kushner’s influence, saying he was “not really directly involved” in the administration, “at least in the day-to-day in the White House,” and again expressed confidence that Republicans could keep control of the House.