In the week following the framework nuclear deal between world powers and Iran, Tehran-based Internet entrepreneur Faty Amir Soleimani pitched every day to Western investors for funding.

“We started getting a lot interest from foreigners,” said Ms. Soleimani, who runs an e-commerce site for baby products called Koodakoo. “When I say a lot, it was really a lot.”

Amid a global glut of investment into Internet companies, Ms. Soleimani’s experience suggests that Western investors are eyeing perhaps their most risky bet yet: Iranian startups.

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