"Clearly this raises serious questions that we have to raise directly with the Saudi government," Clinton said Sunday in response to a Derry town hall question about how she would handle the situation as president.
"We have governments we work with on a number of issues whose policies and values are antithetical to ours, to be just blunt about it. And yet who also have certain interests with us that we are involved in," she said.
Clinton said she joined other leaders in "statements of concern" about the executions, specifically calling out the Obama administration, European governments and human rights groups.
"I think that even our friends who we work with on so many areas should not be immune from our criticism and our questions about rule of law about their treatment of minorities," Clinton added, CNN reported.
The execution prompted the US State Department to call on Saudi Arabia to respect human rights and permit peaceful dissent.
"We are particularly concerned that the execution of (Sheikh Nimr) risks exacerbating sectarian tensions at a time when they urgently need to be reduced," spokesman John Kirby said.
UN Secretary-General Ban Ki-moon was "deeply dismayed" by the executions and called again for an end to the death penalty. He called on leaders in the region to prevent an escalation of sectarian tensions.