He said he expects them to make the same assurances to federal regulators to secure approval for their deal.
"I am pleased with their mitigation plans, but will continue to look for opportunities to improve the government’s existing authorities to thoroughly review all the national security aspects of proposed transactions,” Rogers said.
Sprint and the Justice Department, which is reviewing the deal, declined to comment.
After a yearlong investigation, the Intelligence Committee released a report last year concluding that Huawei and ZTE, another Chinese telecommunications company, pose a threat to U.S. national security and should be barred from doing business in the country.
The panel's report said the two companies failed to provide detailed information about their ties to the Chinese Communist Party, their governance structures or operations in the United States. Huawei has insisted that the report's claims are baseless.
Because Softbank is based in Japan, its purchase of Sprint is automatically under review for any national security concerns.
Bill Plummer, a spokesman for Huawei, said the company hasn't been involved in the review of the Sprint-Softbank deal. He warned that pressuring Sprint to promise not to partner with Huawei would "set a nasty protectionist precedent that could be used against American companies in other markets."
"Given that all suppliers rely on common global supply chains and are subject to common vulnerabilities, it would seem unlikely that any Government would blackball any one supplier because that Government would know full well that this would do absolutely nothing to address security concerns," he said in an emailed statement.
"Indeed, the adoption of such a policy would seem little more than a market-distorting political or protectionist exercise — and one that would require American telecommunications carriers and consumers to sacrifice world-leading technology, innovative, competitive and affordable broadband, as well as jobs and inward investment," he added.