Mr Wright said: "These measures could have a potential impact on the future availability and reliability of, together with other market impacts, and so are relevant considerations in determining Huawei's involvement in the network.
“We have sought clarity on its extent and implications but the position is not yet entirely clear.
"Until it is, we have concluded it'd be wrong to make specific decisions in relation to Huawei but we will do so as soon as possible."
He also told MPs, the Telecoms Supply Chain Review found the "lack of diversity” creates a dependence on single suppliers, posing “a range of risks to the security”.
He added that the UK will pursue a "targeted diversification strategy" to support the "growth of new players in the parts of the network that pose security and resilience risks".
"We will also seek to attract trusted and established firms to the UK market,” he said.
Legislation will also be brought forward to underpin a new set of "telecoms security requirements", overseen by Ofcom and government.
The debate over Huawei's future in the UK as a provider of 5G telecoms equipment has been an ongoing issue, amid fears that it could enable the Chinese government to spy on people in the West - an allegation the firm has repeatedly denied.
Vice president of Huawei Victor Zhang said in a statement: "The evidence shows excluding Huawei would cost the UK economy £7 billion and result in more expensive 5G networks, raising prices for anyone with a mobile device.
"On Friday, Parliament's Intelligence & Security Committee said limiting the market to just two telecoms suppliers would reduce competition, resulting in less resilience and lower security standards.
"They also confirmed that Huawei's inclusion in British networks would not affect the channels used for intelligence sharing."
Labour's Stephen Timms asked if the current situation involving Huawei would delay the rollout of 5G, to which Mr Wright replied: "We have to consider a potential delay to the rollout by any measures that we may decide are necessary.
"I repeat the point that the most important criteria here are that we act in our national security interest.
"If that causes delay then it seems to me that may well be the appropriate course, but we will need to decide that when we are in possession of all of the facts."
Tory MP Dr Julian Lewis said the phrase "manageable risk" - which has been used to describe Huawei's involvement in the rollout of 5G - is a "contradiction in terms", adding: "If it were fully manageable it wouldn't be a risk."
He said: "We would be mad to enter into a direct security relationship with the agencies a totalitarian communist state."
Former defence secretary Gavin Williamson was sacked in May after information was leaked from a top-secret meeting of the National Security Council about Chinese tech giant Huawei.
Allegations of breaching the act were brought against Mr Williamson.
But assistant commissioner Neil Basu said he was "satisfied" that the details disclosed to the media did not "contain information that would breach the Official Secrets Act".