By Jennifer Agiesta, CNN Polling Director

(CNN) -- Two-thirds of Americans, including majorities across party lines, would like to see special counsel Robert Mueller try to finish the investigation into Russian interference in the 2016 election before voters go to the polls to elect a new Congress this November.

That result, from a new CNN poll conducted by SSRS, comes amid rebounding approval ratings for both President Donald Trump and Mueller for their handling of the investigation, and a growing share of voters who say the investigation will matter to their vote this fall.

Trump continues to call into question the validity of the investigation, tweeting regularly that the investigation is a witch hunt and that there was no collusion. But, Trump's lawyers have been negotiating with Mueller's team over a possible sit down with the president.

Most in the poll say the President should testify for Mueller's investigation if asked (70% say so), and the views of that group have shifted as the public wrangling over the terms of an interview has gone on.

Although the overall assessment of the President's handling of the Russia investigation remains largely negative (55% disapprove), his approval numbers have shifted slightly more positive: From 29% approval in June to 34% approval now.

That shift is driven almost entirely by those who think the President should testify. Among that group, 29% now approve of the President's handling of the investigation, up from 20% in June, while among those who say he should not testify, approval has held steady at 52%.

At the same time, Trump's overall approval rating of 42% is about the same as its level this spring, suggesting few opinions have changed as a result of an eventful summer in the White House.

The poll marks the first time that CNN polling has found Trump's approval rating above that of one of his predecessors at the same point in their presidency. Trump's 42% outpaces Jimmy Carter's and Bill Clinton's ratings of 39% each in the August of their second year in office, and narrowly tops Ronald Reagan's 41% rating in August of 1982.

Mueller's ratings have also rebounded in this poll, with 47% now saying they approve of his handling of the Russia investigation, up from 41% in June. That shift stems from a shift among Democrats -- almost three-quarters now approve of Mueller's work, 72%, up 10 points since June.

But Mueller is on the clock: 66% say they think he should try to complete his investigation before this November's congressional elections, while just 26% say that shouldn't be his goal.

Democrats are more apt than Republicans to think Mueller shouldn't aim to wrap it up before the elections (34% of Democrats say so vs. 24% of independents and 23% of Republicans), but majorities across parties say he ought to try to complete the investigation before voters head to the polls (72% of Republicans, 57% of Democrats and 69% of independents).

At the same time, the percentage of voters who say the investigation will be extremely important to their vote this fall has risen 7 points to 30%. It is most likely to be of deep importance to Democrats (55%, up from 39% saying the same in May) and those who disapprove of Trump (49%, up from 35%).

On other questions about the Russia investigation, public opinion continues to largely hold steady.

About 6 in 10 say the investigation itself is a serious matter that should be fully investigated, while 4 in 10 say it's mainly an effort to discredit Trump's presidency, numbers that have remained nearly constant since last summer. A majority (56%) say they think Trump has attempted to interfere in the investigation, about the same as said so in February (55%). Most think Trump's public statements about the investigation are largely false (56%, same as in December), and that he did know during the 2016 campaign that anyone associated with his campaign had contact with suspected Russian operatives (57%, about the same as the 59% who said so in November).

About half of Americans (47%) say they are following Paul Manafort's trial on financial fraud charges closely, 53% say they are mostly tuned out. Democrats are more apt to be following along than are Republicans (59% among Democrats, 45% among Republicans and just 39% of independents say they are following the trial closely).

The CNN poll was conducted by SSRS August 9-12 among a random national sample of 1,002 adults reached on landlines or cellphones by a live interviewer. Results for the full sample have a margin of sampling error of plus or minus 3.9 percentage points, it is larger for subgroups.