Dissatisfaction with President Obama’s conduct of foreign policy has shot up among both Republicans and Democrats in the past month, even though a slim majority supports his recent decision to send military advisers to Iraq to confront the growing threat from militants there, according to the latest New York Times/CBS News poll.

The survey suggests that most Americans back some of Mr. Obama’s approaches to the crisis in Iraq, including majority support for the possibility of drone strikes. But the poll documents an increasing lack of faith in the president and his leadership, and shows deep concern that further intervention by the United States in Iraq could lead to another long and costly involvement there.

The poll found that 58 percent of Americans disapprove of the way Mr. Obama is handling foreign policy, a jump of 10 points in the last month to the highest level since Mr. Obama took office in 2009. The spike in disapproval is especially striking among Democrats, nearly a third of whom said they did not approve of his handling of foreign policy.

Fifty-two percent of Americans say they disapprove of how the president is dealing with the current violence in Iraq (including about a third of Democrats); 37 percent approve.