Former US President Barack Obama warned Democratic presidential candidates of a policy that was not "rooted in reality".
Obama said Democrats risked alienating voters if they went too far to the left.
The former president said in a fundraiser that most voters did not want to "tear down" the system.
Obama has not publicly supported a Democratic candidate.
The field is overcrowded. 1
Leaders include former Vice President Joe Biden, Senators Elizabeth Warren and Bernie Sanders, and Pete Buttigieg, Mayor of South Bend, Indiana
On Friday in Washington, Obama did not mention a candidate by name, nor did he criticize a specific political proposal. Instead, he used the semblance to urge the Democrats to "pay some attention" to vote on topics such as health care and immigration.
These voters, Obama says, do not necessarily have the same views as what he called "certain left-wing Twitter feeds" or "the activist wing of our party."  The comments, less than four months before the Democratic primary, represent one of Mr. Obama's most significant interventions in the race so far.
They can be viewed as criticizing Senators Sanders and Warren – widely considered to be two of the left-most radical candidates in the field.
Both candidates have so far called for political and economic change, including measures to end private health insurance and to decriminalize illegal border crossings.
But Obama, who occupied the White House from 2009 to 2017, said the country was "less revolutionary than it interests me."
"Even if we push the envelope and our vision is courageous we also be rooted in reality, "said Obama at the meeting, which reportedly involved wealthy liberal donors.
The Democratic race is still largely in the air, though the first federal-state poll will decide which candidate will face Trump for the White House in Iowa in February.
Some Democrats fear that moderate Mr. Biden will have trouble defeating Mr. Trump, causing a flood of newbies to join the race.
Over the past few days, former Massachusetts Governor Deval Patrick has entered the field amid speculation that former New York Mayor Michael Bloomberg may follow suit.
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Meanwhile, political rumors over whether Hillary Clinton could enter the conflict continue to push his tongue in Washington DC.
In an interview with the BBC, Ms. Clinton said she was "under tremendous pressure" to challenge Mr. Trump, who defeated her in the 2016 presidential election.
Who will have to compete with Trump in 2020?
Election day is less than In a year the time has come and the race for Democratic challenger Donald Trump is growing.
Recent polls indicate that Joe Biden and Elizabeth Warren are the frontrunners, while Bernie Sanders and Pete Buttigieg are not far behind.
- Learn about the competitors