Story highlights Narrow majority thinks the President attempted to interfere with investigation

Robert Mueller's approval rating holds steady over the last month

WASHINGTON (CNN) Almost 8 in 10 Americans say President Donald Trump should testify under oath if asked to do so for the investigation being run by special counsel Robert Mueller, including majorities across party lines, according to a new CNN poll conducted by SSRS.

Overall, 78% say Trump ought to testify in the inquiry focused on Russian efforts to interfere with the 2016 US election if he is asked. That rises to 95% among Democrats, while standing at 75% among independents and 59% among Republicans.

The findings come after news that a member of Trump's Cabinet, Attorney General Jeff Sessions, answered questions from Mueller's team for several hours last week. Other members of Trump's inner circle are reported to have spoken with investigators working on the probe recently as well, including the president's son-in-law, Jared Kushner, White House communications director Hope Hicks and White House counsel Don McGahn. While the poll was in the field, news emerged that former White House chief strategist Steve Bannon had agreed to speak with Mueller's team as well.

The public is more closely divided on whether the President himself has attempted to interfere with the investigation: 51% say he has, 41% say he has not. The partisan divide on this question is especially sharp, with 83% of Democrats saying Trump has attempted to interfere with the investigation and 82% of Republicans saying he has not done so.

Read More