English Football League chairman Rick Parry says coronavirus testing will increase after Cheltenham's League Two match with Grimsby became the latest to be postponed.
Grimsby have told the EFL that they are unable to safely fulfil the fixture as a player has tested positive for Covid-19.
Leyton Orient's trip to Walsall had already been postponed due to a number positive cases within the O's squad, which also forced their Carabao Cup tie with Tottenham to be called off, while Stevenage's match at Bradford is in jeopardy after one of their players tested positive.
Parry told the Daily Mail: "Safety absolutely comes first and foremost.
"We obviously had a major problem at Leyton Orient. I don't think we needed a wake-up call but it has given us one.
"We were following the medical guidance and there were so few positive tests last season in the Championship that the advice was you don't need to be testing all the time if you are following the protocols. If you are monitoring symptoms, then testing all the time isn't essential.
"We are now reviewing, particularly now that the infection rate is rising. There is no room for any complacency. We will do some increased testing. Maybe it will be random, maybe it will be periodic.
"But, again, the real message is everyone has to stick to the protocols and observe them. If you don't then things can go quickly wrong. The infection rates being what they are, you have got to think of the nation and we can't put pressure on the NHS again."
An EFL statement earlier on Friday read: "This weekend's Sky Bet League Two fixture between Cheltenham Town and Grimsby Town has been suspended and will not take place on Saturday as scheduled.
"Due to a positive case of Covid-19 being identified within the Grimsby Town squad it has resulted in other players and staff being required to self-isolate in line with EFL and Government guidance.
"As a result, the club has advised the EFL it considers it is unable to safely fulfil this weekend's fixture.
"The circumstances surrounding the postponement will now be the subject of an investigation in accordance with EFL regulations."
At Stevenage a player reported mild Covid-19 symptoms on Thursday and subsequently tested positive.
The club cancelled travel plans to Bradford and tested all their players and staff, with the results due on Saturday morning.
Stevenage chairman Phil Wallace has called for support in order to get weekly testing, in line with Premier League clubs.
He told the club website: "When it happens in your club, you feel an obligation to test everyone, if only to reassure them. But what do we do if another individual reports with symptoms on Monday – test everyone all over again?
"This isn't the right way and nor is only testing symptomatic players. The EFL simply can't leave it to clubs to decide who gets tested and who doesn't for all sorts of fairly obvious reasons.
"With what's in front of us, I believe we have to find a way to get weekly testing funded."
Rochdale chief executive David Bottomley added: "Weekly testing has to happen. It's a very expensive procedure, because you're looking at that adding another £15,000 a month to a normal everyday operation.
"But I think for the continuation of football, behind closed doors even, players and associated staff have to be tested, no question."
