Johnson said on Monday it was possible to keep up with new 5G technology without compromising national security or Britain's deep intelligence relationship with the United States.
"We are going to come up with a solution that enables us to achieve both those objectives," he said in reply to a reporter's question about Huawei.
Huawei, the world’s biggest producer of telecoms equipment, says the United States wants it blocked from Britain's 5G network because no U.S. company can offer the same range of technology at a competitive price.
5G is one of the biggest innovations since the birth of the internet a generation ago, offering consumers and businesses much faster data speeds.
In what some have compared to the Cold War arms race, the United States is worried that 5G dominance would embed China into global communications networks, giving it an unassailable technological and security advantage.
Sources told Reuters last week senior British officials had proposed granting Huawei a limited role in the 5G network - a "calculated compromise" which could be presented to Washington as a tough restriction but also accepted by British operators already using the company's equipment.
Huawei's equipment is already used by Britain's biggest telecoms companies such as BT and Vodafone, but it has been largely deployed at the "edge" of the network and excluded in the "core" where data is processed.
The United States has argued that as 5G technology evolves, the distinction between the "edge" and "core" will blur as data is processed throughout the network, making it difficult to contain any security risks.
Tom Tugendhat, a Conservative former head of the British parliament's foreign affairs committee, compared giving Huawei access to Britain's 5G network to "allowing the fox into the hen house when really we should be guarding the wire".
But telecoms companies have warned that it will cost them billions of dollars and delay the roll-out of 5G if Huawei is banned completely. It would leave them reliant on Sweden's Ericsson and Finland's Nokia, the only major competitors to the Chinese giant.
British intelligence officials have criticised Huawei for failing to address security flaws in its equipment, but say they have found no evidence of state espionage and believe they are able to successfully manage any risks posed by the firm.
"There's a disconnect between a political conversation and a technical one, which is making it very hard for the UK to move forward on this issue," said Malcolm Chalmers, deputy director-general of the Royal United Services Institute and an adviser to parliament's joint committee on national security strategy.
The debate over Huawei's role in 5G networks has split opinion across Europe, with politicians weighing the U.S.-led arguments against lucrative trade ties with China.
Former Prime Minister Theresa May agreed last year before leaving office to block Huawei from all core parts of the 5G network, but to give it restricted access to non-core parts.
(Reporting by Jack Stubbs, Luke Baker, Kylie MacLellan and Paul Sandle; Editing by Timothy Heritage/Guy Faulconbridge/Alexander Smith) ((email@example.com; Reuters Messaging: firstname.lastname@example.org))