House Speaker Nancy Pelosi and rebellious freshman Rep. Alexandria Ocasio-Cortez will hold a sit-down this week to try to sort out their feud, hoping to prevent it from boiling over during their looming lengthy summer vacation.

The relationship between the women has grown strained amid suggestions of racism and intense battles over how far left the Democratic Party can, and should, tilt.

Left-wing activists say they don’t mind Mrs. Pelosi cracking heads within her party’s caucus, but they add that she has been going after the wrong targets when she tries to minimize the legislative heft of Ms. Ocasio-Cortez and several other freshman women who have dubbed themselves “The Squad.”

“The big sin of Pelosi’s swipe at AOC and The Squad is the marginalizing of true leaders that millions of people look up to,” Adam Green, co-founder of the Progressive Change Campaign Committee, told The Washington Times. “We would like her to call out people. She should just aim her fire at the right people.”

The right people, he said, are the more moderate members of the House Democratic Caucus, who built the majority that gave Mrs. Pelosi back the speaker’s gavel but who aren’t as eager to tilt as far to the left as the more vocal liberals, such as Ms. Ocasio-Cortez of New York and Reps. Ilhan Omar of Minnesota, Ayanna Pressley of Massachusetts and Rashida Tlaib of Michigan.

The feud has infected policy and rhetoric.

Mrs. Pelosi, outmaneuvered by President Trump on the border crisis spending bill, was forced to approve a bipartisan $4.6 billion Senate measure that many in her party’s left-wing felt gave too much money, without enough new restrictions on how the administration should conduct immigration enforcement.

Moderates sank Mrs. Pelosi’s efforts to try to force a last-minute negotiation with the Senate.

Ryan Greenwood, director of Movement Politics for People’s Action, said those moderates “are no way in line” with the rest of the party.

He said the group plans to step up political pressure on moderates to try to force them to back the liberals’ agenda.

The rhetorical sniping between Ms. Ocasio-Cortez and Mrs. Pelosi surged in recent weeks after Mrs. Pelosi, frustrated at the criticism of her handling of the border bill, dismissed the four freshman women’s clout as “their Twitter world.”

Ms. Ocasio-Cortez fired back by suggesting that Mrs. Pelosi was singling out racial and ethnic minority women for her criticism. She quickly had to backtrack and insisted that she didn’t think Mrs. Pelosi was racist.

Democrats insisted last week that the feud was overblown and the caucus was past it.

Heads of the big ideological caucuses issued a joint statement that acknowledged “there may be different perspectives on the way forward” but called it part of the give and take of the “legislative process.”

“We will remain clear-eyed with respect to our unity of purpose. Every single voice within the House Democratic Caucus is an important one. We have a shared mission. Onward and upward,” wrote House Democratic Caucus Chairman Hakeem S. Jeffries of New York, Congressional Progressive Caucus Co-Chairs Ramila Jayapal of Washington and Mark Pocan of Wisconsin, New Democrat Coalition Chair Derek Kilmer of Washington and Blue Dog Coalition Chair Stephanie N. Murphy of Florida.

Several incendiary tweets were quietly deleted from various offenders’ accounts.

Among them was one by Mr. Pocan calling a caucus of moderates the “child abuse caucus,” one by Ms. Ocasio-Cortez’s chief of staff, Saikat Chakrabarti, calling the moderate Blue Dog Democrats racists, and one by the official House Democratic Caucus Twitter account that had blasted back at Mr. Chakrabarti.

Heading into this week’s meeting between Mrs. Pelosi and Ms. Ocasio-Cortez, liberal activists said the burden is on Mrs. Pelosi to patch up differences and tilt House Democrats to the left.

“If Nancy Pelosi does not think that issues of corporate accountability and Trump accountability are popular with the American people, that’s just a broken conventional wisdom,” Mr. Green said. “I think there will probably be more soul searching from progressives in the next leadership contest.”

Mr. Greenwood said Democrats have a built-in point of unity: Mr. Trump.

“We’re going to have disagreements in a progressive movement all the time. But it’s clear that the out and out racism of our president is one of the most important and terrifying things in American life. That’s the priority in our book,” he said.

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