By Eugene Scott

CNN

(CNN) -- President Donald Trump's job approval rating has dropped to 36% due to Americans' negative reaction to his handling of the Russia investigations, a new CBS News poll has found.

When CBS last polled Trump's job approval rating in late April, his approval rating was 41%. The drop is partially due to his dwindling support among Republicans.

In the poll released Tuesday, a third of Americans say Trump's approach to the Russia investigation has worsened their opinion of him. With 63% of Americans disapproving of Trump's response to the Russia investigation, the President's handling of the matter has gotten lower marks than his handling of other issues, including the economy and terrorism.

Most people in both parties -- 56% -- believe that Special Counsel Robert Mueller's investigation will be impartial and that Trump should not attempt to stop it.

However, there are divisions among how people respond to the Russia investigation. Most Americans who approve of Trump say the Russia investigation is not serious and they feel the President is being criticized more than his predecessors. Those beliefs cause them to back the President even more.

Another CBS poll found that most Americans -- 73% -- would prefer a public discussion on the Republicans' health care replacement bill and feel they don't have a good understanding of what the new plan would do. By a two to one margin, more people believe the Republicans' plan would hurt them more than help them.

The poll was conducted by telephone from June 15 to 18 among a random sample of 1,117 adults nationwide. Phone numbers were dialed from samples of both standard land-line and cell phones.