Since clinching nomination in early June, Clinton's favourable ratings among Democrats and Democratic-leaning independents have gone up slightly to 71%, compared with 68% in April and May, the survey said.
68-year-old Clinton's image is now partly restored to what it was at the start of the year when 74% of Democrats viewed her favourably.
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Trump's favourable ratings among Republicans averages 64% so far in June, the same as in May but higher than the 54% to 56% in the three prior months.
His current favourable ratings also exceed the average 61% he earned from this partisan group in January, the survey noted.
Clinton, 68, and Trump, 70, have each lost ground over the course of 2016 among independents who lean toward neither party.
"Because of this, the candidates' national favorable ratings have stayed still or declined slightly, despite recent improved ratings from their own partisans," it said.
Clinton's overall favorable ratings since clinching the nomination have averaged 41%, nearly matching her 40% in May but down slightly from 44% in January.
Trump's average 31% thus far in June compares with 32% in May and 34% in January.
However, the electoral importance of pure independents will likely be muted as Gallup polling traditionally shows this group to be less engaged in politics and less likely to vote than those who identify with or lean toward one of the two major parties, it said.
Gallup is an American research-based, global performance-management consulting company. Founded by George Gallup in 1935, the company is known for its public opinion polls conducted in several countries.
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