Citizens from Australia, Britain and Poland were among seven people working for World Central Kitchen who were killed in an Israeli airstrike in central Gaza on Monday, the NGO said.
Sunak said he was "shocked and saddened" and the government was working to urgently to verify all the details.
"We're asking Israel to investigate what happened urgently, because clearly there are questions that need to be answered," Sunak told reporters during a visit to northeast England.
He said aid workers were doing "fantastic work" to alleviate suffering in Gaza.
"They need to be allowed to do that work unhindered. And it's incumbent on Israel to make sure that they can do that," he said.
British foreign minister David Cameron said earlier that Britain had called on Israel to immediately investigate and provide a "full, transparent explanation of what happened."
(Reporting by Sachin Ravikumar; Editing by Kate Holton)
