By Susan Heavey and Susan Cornwell

WASHINGTON (Reuters) - Another Republican senator has moved closer to re-election while keeping some distance from Donald Trump, and experts say this suggests the party's presidential candidate may be having little down-ballot impact, at least at the primary stage.

Senator Kelly Ayotte of New Hampshire still faces a tough general election challenge on Nov. 8, but on Tuesday she crushed a pro-Trump, Republican challenger in a primary contest.

Ayotte garnered close to 80 percent of the vote. She has refused to endorse Trump, though like a number of Republicans, she has said she will vote for him.

Some Republicans, such as Ohio Senator Rob Portman, have endorsed Trump, but excluded him from their campaigns. Senator Lisa Murkowski of Alaska won her primary in August although she had said she did not know whether she would vote for Trump.

Trump, a New York businessman who has never held elected office, at first attacked Ayotte. Then early last month he changed course and endorsed her, along with fellow Republicans House Speaker Paul Ryan and Senator John McCain.

With Ayotte's victory, all incumbent Republican senators running for re-election have won their primaries this year. This is not uncommon, but it is unusual for so many senators to hold their party's presidential nominee at arm's length.

U.S. senators serve six-year-terms. One-third of the 100-member Senate faces voters every two years.

The outcome so far shows some voters are distinguishing this year between Trump and the rest of the ballot, said Nathan Gonzales, editor of The Rothenberg & Gonzales Political Report, a nonpartisan newsletter.

"His impact has been less dramatic than what was initially expected, but there is still time for things to get worse for the Republican Party," Gonzales said in a telephone interview.

“At a time when Republicans in presidential primaries basically rejected everybody from the status quo, they are not doing that in Senate or House primaries,” Norman Ornstein, a political scientist at the American Enterprise Institute, a conservative think tank, said by phone.

Republicans are still worried that voters who do not like Trump will not turn out to vote for other Republicans in the general election on Nov. 8, Gonzales said.

"Is there a Trump drag (on down-ballot candidates)? There doesn't appear to be much of one," said Jennifer Duffy, senior editor at the non-partisan Cook Political Report.

Ohio's Portman, who has not appeared with Trump on the campaign trail, easily beat his primary opponent and has opened up a lead over his Democratic challenger in the general election.

McCain and Ryan have had very public differences of opinion with Trump, but they also prevailed in their primary races.

In New Hampshire, Ayotte beat her main primary challenger Jim Rubens by 78.9 percent to 17.4 percent, with 99 percent of precincts reporting, according to media reports citing the Associated Press.

Ayotte still must take on Democratic New Hampshire Governor Maggie Hassan in the general election. Ayotte was leading Hassan by 52 percent to 44 percent in a Sept. 6-8 NBC/Wall Street Journal/Marist poll, according to the website RealClear Politics.

"I think you probably have a lot of people in the primary, who were not going to pay as close attention to what she was saying about Trump," Ornstein said of Ayotte. "In the fall it may be a different matter, as certainly Maggie Hassan is going to try to tie her to Trump.”

(Editing by Kevin Drawbaugh and Jonathan Oatis)