WASHINGTON (CNN) Former Vice President Joe Biden's lead in the race for the Democratic nomination for president has rebounded, and now stands at its widest margin since April, according to a new CNN poll conducted by SSRS .

Biden has the support of 34% of Democratic and Democratic-leaning registered voters, his best showing in CNN polling since just after his campaign's formal launch on April 25.

Sens. Elizabeth Warren of Massachusetts and Bernie Sanders of Vermont are about even for second, with 19% and 16%, respectively. Behind them, South Bend, Indiana, Mayor Pete Buttigieg and Sen. Kamala Harris of California each have 6% support, with Sen. Amy Klobuchar of Minnesota and former Texas Congressman Beto O'Rourke each at 3%.

Biden's rise comes largely from a consolidation of support among his core backers, and doesn't appear to harm any individual opponent. Warren and Sanders hold about even with their standing in the last CNN poll in September, and no other candidate has seen a shift of more than 2 points in that time.

But Biden has seen big spikes in support among moderate and conservative Democrats (43% support him now, up from 29% in the September poll), racial and ethnic minorities (from 28% among all nonwhites in September to 42% now) and older voters (up 13 points since September among those 45 and older) that outpace those among younger potential Democratic voters (up 5 points among those younger than 45).

The gains come as Biden's time as vice president is put under the spotlight by President Donald Trump and his allies. Trump is facing an impeachment inquiry by the House of Representatives over allegations that he pressured the Ukrainian government to investigate Biden and his son, Hunter Biden, as well as the 2016 US election in return for releasing hundreds of millions in congressionally mandated defense funding meant for Ukraine. Hunter Biden was on the board of a Ukrainian natural gas company while Biden was vice president. There is no evidence that either Biden did anything wrong in Ukraine.

The poll suggests that although Biden's October debate performance did not blow away the audience (15% who watched or followed news about it said he had done the best job in the debate, well behind Warren's 28% -- but better than most on the stage), the arguments he made on health care, foreign policy and the economy may have boosted his standing with the potential Democratic electorate.

Asked which candidate would best handle a range of top issues, Biden leads the way on four of the six issues tested in the poll. He holds a massive edge over the field on foreign policy (56% say he would handle it best, well ahead of Sanders at 13% and Warren at 11%), and tops the next closest candidate by nearly 20 points on the economy (38% Biden, 19% Sanders, 16% Warren). Biden also outpaces the rest of the field as most trusted on immigration (29% Biden, 16% each Warren and Sanders) and gun policy (27% vs. 13% Sanders and 11% Warren, with O'Rourke close at 9%).

Biden doesn't hold a significant edge on the critical issue of health care (31% Biden, 28% Sanders, 17% Warren) but he's surged 13 points on the issue since June, when he lagged behind Sanders. Neither Sanders' nor Warren's numbers on the issue have moved significantly in that time.

And Biden now runs even with Sanders at 26% as best able to handle the climate crisis. Warren is at 18% on that issue. The results mark increases for Biden and Sanders, who were each at 19% on handling the climate in June.

The former vice president's advantages on the issues come as he emphasizes an approach that appears to align with the preferences of most potential Democratic voters. A 53% majority say they want the nominee to advocate policies that have a good chance of becoming law, even if the changes aren't as big, vs. 42% who prefer advocating big changes even if they have less of a chance of becoming law.

Among those voters who prefer an approach that prioritizes policies with a better chance of becoming law, 38% support Biden for the Democratic nomination, 17% Warren and just 8% Sanders. On the other side, it's nearly a three-way split, with 27% behind Biden, 24% Sanders and 21% Warren.

About 1 in 5 potential Democratic voters say they watched last week's debate among 12 Democratic candidates, and those who watched it came away with a different assessment than those who mainly followed news about the debate. Overall, among everyone who either watched or followed news coverage on the debate, 28% say Warren had the best night, 15% Biden, 13% Sanders, 11% Buttigieg, 4% Klobuchar and 2% Sen. Cory Booker of New Jersey, with the rest at 1% or less. Among those who say they watched it, though, Warren remains on top at 29%, but 21% say Buttigieg had the best night, then 13% Biden, 11% Sanders, 10% Klobuchar and 4% Booker, with everyone else at 1% or less.

And those who watched the debate seem to have more favorable views of the lesser-known candidates who were seen as having good nights than do those who followed coverage. Among debate watchers, 74% have a favorable view of Buttigieg, vs. 54% among those who followed news instead. Booker's favorability rating is 80% among those who watched, vs. 55% among those who followed coverage, and Klobuchar's favorability stands at 56% among watchers vs. 36% among those who followed news.

Warren tops the list of candidates who potential Democratic voters say they want to hear more about: 31% name her, 24% Buttigieg, 23% Harris, 18% Booker, 17% Sanders, 16% Biden, 13% Klobuchar, 11% O'Rourke and 10% businessman Andrew Yang.

Majorities of potential Democratic voters say they would at least be satisfied with any of the top three becoming the party's nominee, with about 4 in 10 saying they'd be enthusiastic about Biden (43%), Warren (41%) or Sanders (39%). Fewer would feel as excited should Buttigieg become the party's nominee (27% enthusiastic).

Registered voters generally give Biden, Warren, Sanders and Buttigieg large advantages over President Donald Trump in hypothetical general election matchups. Biden leads the President by 10 points, 53% to 43%, with Sanders up 9 (52% to 43%) and Warren up 8 (52% to 44%). Buttigieg holds a 6-point edge, 50% to 44%.

The CNN Poll was conducted by SSRS from October 17 through 20 among a random national sample of 1,003 adults reached on landlines or cellphones by a live interviewer, including 424 registered voters who are Democrats or Democratic-leaning independents. Results for the full sample have a margin of sampling error of plus or minus 3.7 percentage points. For results among potential Democratic voters, it is plus or minus 5.8 points.