(CNN) In the first national telephone poll since Donald Trump earned rebukes from Republican leaders over his comments about Senator John McCain's military service, the real estate mogul has increased his support among GOP voters and now stands atop the race for the party's nomination.

The new CNN/ORC Poll finds Trump at 18% support among Republicans, with former Florida governor Jeb Bush just behind at 15%, within the poll's margin of error.

They are joined at the top of the pack by Wisconsin Governor Scott Walker, with 10% support among Republicans and Republican-leaning independents who are registered to vote. Trump's backing has climbed 6 points since a late-June poll, while support for Bush and Walker has not changed significantly.

None of the other 14 candidates tested in the new CNN/ORC survey earned double-digit support.

Though Trump currently tops the race for the nomination, his advantage is by no means firm. A majority of Republican voters, 51%, say they see the field as wide open, and that it's too soon to say which candidate they will ultimately get behind. Among that group that see the contest as wide open, Bush has 14% support, while Trump has the backing of 13% and Walker stands at 9%.

Trump does much better among those Republicans who say they've narrowed it down to one or two candidates, 24% of that group backs him, 16% Bush and 12% Walker.

Trump's popularity among Republican voters does not translate to the broader pool of registered voters. When tested in hypothetical general election matchups against top Democrats, he trails both frontrunner Hillary Clinton and upstart Senator Bernie Sanders by wide margins. Bush and Walker run just behind Clinton and about even with Sanders.

Trump's unfavorability rating is sky high. Overall, 59% of all registered voters have an unfavorable opinion of Trump, though that dips to 42% among GOP voters.

None of the other Republicans landing near the top of the field have such a negative image nationwide, though many remain little known.

Clinton is the only candidate who is about as well-known as Trump, and while she is more well-liked than the developer, her favorability rating is net negative among registered voters nationally: 49% have an unfavorable view while 44% have a positive impression.

Still, the poll suggests Republican voters haven't yet had their fill of Trump. A majority (52%) say they'd like to see Trump continue his run for the GOP nomination, including nearly six in 10 conservatives, tea party supporters and white evangelicals. Even among those Republican voters who support someone other than Trump, 42% say they'd like him to remain in the field.

The Republican electorate is more enthusiastic about next year's vote than the Democrats are. The poll finds 46% of Democratic voters say they are extremely or very enthusiastic about voting for president next year, compared with 55% of Republican voters. But enthusiasm is down in both parties compared with June of 2011, when 61% of Republican registered voters and 55% of Democratic registered voters were that enthusiastic.

In another positive sign for Trump's candidacy, among those Republicans who are enthusiastic about voting next year, Trump holds a larger edge over his competition: 22% say they would back him for their party's nomination, compared with 14% who back Bush and 12% behind Walker.

Overall, about three-quarters of Republicans are satisfied with their choices, more so than in 2011 at this time (about two-thirds were satisfied then), but still, just 23% say they are "very satisfied" with the field.

Meanwhile, an NBC News/Marist poll on Sunday showed Trump leading among New Hampshire GOP primary voters and narrowly trailing Walker in Iowa.

Trump took 21% of the New Hampshire GOP primary vote, with Bush running second at 14%, while in Iowa Trump was at 17% and Walker at 19%, according to the NBC/Marist survey

On the Democratic side, the CNN poll found Clinton remains the clear frontrunner, though Sanders has increased his support slightly since last month's poll. Clinton is backed by 56% of registered Democratic and Democratic-leaning voters, while Sanders has inched up to 19% from 15% in June. The rest of the field is about even with where they were before.

The CNN/ORC International Poll was conducted July 22-25 among a random national sample of 1,017 adults, including 898 registered voters. Results for all registered voters have a margin of sampling error of plus or minus 3.5 percentage points. The registered voter sample included 419 Republicans and Republican-leaning independents as well as 392 Democrats and Democratic-leaning independents.