LOS ALTOS HILLS, Calif. — Former President Barack Obama urged Democrats on Thursday to “chill out” about the party’s 2020 field and to avoid putting candidates through “purity tests,” and warned that average voters were “nervous about changes that might take away what little they have.”

Speaking to party donors a day after the latest Democratic primary debate, Mr. Obama added to a series of recent remarks about American politics and the presidential race, including his warning on Friday that the candidates not move too far to the left in their policy proposals and his observation that the average American does not want to “tear down the system.”

Mr. Obama’s comments on Thursday appeared at times aimed more at Democratic officials, activists and donors than at the candidates themselves. Democrats should focus less on the “tactical disagreements” among the candidates, Mr. Obama said, and avoid making false choices between appealing to white working class voters or minority voters, or between energizing the party’s base or reaching out to independents and Republicans.

“Everybody needs to chill out about the candidates, but gin up about the prospect of rallying behind” a candidate , Mr. Obama said.