Eighteen liberal advocacy groups are banding together to call for unity and try to rally against candidates supported by the “corporate wing” amid the recent spat between Sen. Bernard Sanders of Vermont and Sen. Elizabeth Warren of Massachusetts.

Calling the mission “Progressives Unite 2020,” the groups are urging people to take a pledge “to focus our fight for the nomination against candidates supported by the corporate wing, instead of fighting each other.”

“When progressives fight each other, the establishment wins,” said Charles Chamberlain, chairman of Democracy for America. “We saw it in 2004 when progressives took each other out and John Kerry slipped through to win Iowa and then went on to lose in November to a very unpopular Republican incumbent. We’re determined to not let that happen again.”

DFA supported Mr. Sanders in 2016, but does not plan to throw official support to a candidate before Iowa. Other groups that have endorsed both Mr. Sanders and Ms. Warren for the 2020 Democratic presidential nomination are part of the effort.

The coalition included a guide for the Iowa caucuses instructing people who take the pledge to support either Mr. Sanders or Ms. Warren if their candidate of choice does not hit the 15% “viability threshold” needed to continue.

Other signatories include Center for Popular Democracy Action and Sunrise Movement, which have endorsed Mr. Sanders, as well as the Progressive Change Campaign Committee and Working Families Party, which have endorsed Ms. Warren.

The push comes amid heightened tensions between the two liberal allies after Ms. Warren said this week that Mr. Sanders told her in a 2018 meeting that a woman couldn’t be elected president.

Mr. Sanders denied making such a remark — a statement he repeated at Tuesday’s debate.

At the debate, Ms. Warren stuck by her previous statement on the meeting and pointed to all the election losses the men on the stage had racked up to prove her point that a woman could win.

On Wednesday evening, CNN released audio from an exchange between the two candidates after the debate in which Ms. Warren is heard saying that Mr. Sanders called her a “liar” on national TV.

“I think you called me a liar on national TV,” she told him.

“What?” he said.

She repeated: “I think you called me a liar on national TV.”

“Let’s not do it right now. You want to have that discussion, we’ll have that discussion,” Mr. Sanders said.

“Anytime,” Ms. Warren said.

“You called me a liar. You told me—” he said. “All right, let’s not do it now.”

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