The new Labour leader has appealed for “transparency and openness” on plans to end lockdown measures in the UK.
Sir Keir Starmer said it was “not realistic” to put a date on the move, but believed “the principles” should be shared by the government.
He also said ministers should be clear about who was in charge if Boris Johnson was recuperating for some time.
Foreign Secretary Dominic Raab is deputising for the prime minister while he is treated in hospital.
Mr Raab said on Thursday that a decision on whether to ease lockdown measures would not come until “the end of next week”.
Sir Keir said: “We need to know how long he [Mr Johnson] is going to be out of action and the government needs to put in place sensible arrangements, if it’s likely to be weeks, and it could be.
“We need robust replacement arrangements in place and we need to know what they are, as soon as possible.”
Shadow foreign secretary Lisa Nandy has called on Mr Raab to name a replacement to run the Foreign and Commonwealth Office (FCO) while he is covering for the PM.
She said coordinating the fight against coronavirus will “rightly demand the full attention of Dominic Raab and his team”.
But Ms Nandy said it was a “global crisis and demands a global response”, with leadership from the FCO.
After Mr Johnson brought in tougher measures to try to control the spread of the virus, he confirmed the move would be reviewed three weeks later – or this coming Monday.
Speaking at the daily press briefing, Mr Raab would not confirm the government’s plans.
But he stressed that the lockdown restrictions would have to stay in place until evidence showed the UK had moved beyond the peak of the virus.
Mr Raab said: “After all the efforts everybody has made, after all the sacrifices so many people have made let’s not ruin it now.”
Sir Keir said he “completely understands” why the government cannot provide a timetable yet.
But he said the public “need these questions answered” and, by being transparent, the government was “much more likely to get their trust”.
He added: “That’s why I’m pushing the government to publish and tell people what is the exit strategy, the principles, not the precise timing.”
A No 10 spokesman confirmed work was taking place across Whitehall on the exit strategy, but said they would not set out the details until the right moment.