Boris Johnson should take questions from a group of senior MPs twice a week while Parliament is shut, one Conservative MP has said.
Ex-Defence Minister Tobias Ellwood says this would ensure “partial scrutiny” can continue.
Parliament has closed for one month to combat the spread of coronavirus.
But some MPs have expressed concern that this will prevent the government from being held to account for its decisions.
The House of Commons had been due to break for Easter on 31 March, but shut down on 25 March instead.
Commons leader Jacob Rees-Mogg said the “aim” was for MPs to return to work on 21 April, but added he would “keep the situation under review in terms of medical advice”.
The closure followed concerns that Parliament had become a hotspot for the coronavirus with a number of MPs self-isolating after displaying symptoms.
But some MPs questioned the decision arguing it risked undermining the Commons’ role as a scrutinising body at a time of national crisis.
Labour’s Wes Streeting said he felt “very uncomfortable” that the Commons would start recess before the government announced its package to help the self-employed. MPs ability to question ministers will be “diminished”, he said.
Another Labour MP, Barry Sheerman, called for “new ways of maintaining proper scrutiny of the government”.
Mr Ellwood also questioned the decision, tweeting: “The national crisis continues, the country is on lockdown – yet Parliament breaks for four weeks.”
“I’ve written to the PM asking for two online meetings a week with all select committee chairs so partial scrutiny of the executive by the legislative can continue during recess.”
The Liaison Committee is made up of the select committee chairs and traditionally takes evidence from the PM a couple of times a year.
Mr Johnson is yet to face the committee and has in the past been criticised for cancelling scheduled hearings.
Speaking at Prime Minister’s Questions on Wednesday, Mr Johnson promised to work with the Commons Speaker to ensure Parliament is kept informed.
Despite the closure of Parliament some committees are still taking place.
On Thursday, the health committee held an evidence session in which both witnesses and MPs took part remotely.
Speaker Sir Lindsay Hoyle told MPs work would take place throughout the break to ensure they had the technology they need to stay connected, and he expressed the hope that, with the government’s help, they could create “the virtual parliament and virtual select committees”.
And speaking to the Today programme on BBC Radio Four, Sir Lindsay said accountability was important but added “we’ve got to be careful we don’t tie ministers down so they don’t get on with their job.”
“Getting the balance right is important,” he added.