The Cabinet minister issued his latest plea for Peter Hebblethwaite to quit on Wednesday, claiming “he will have to go”.
But the ferry operator said calls for Mr Hebblethwaite to step down “need to stop”.
Despite the attempts from some parties to undermine our business by creating false rumours and uninformed commentary, our morale is high and our spirit as a company is strong
Its decision to sack 786 crew members without notice and replace them with cheaper agency workers was widely condemned.
Mr Hebblethwaite admitted to MPs last month that the firm broke the law by not consulting trade unions, leading Mr Shapps and other politicians to call for him to resign.
Giving evidence to the Commons Transport Select Committee on Wednesday, Mr Shapps said it is “completely unsustainable” for Mr Hebblethwaite to keep his role.
After the session, a spokesman for P&O Ferries said: “The actions our company took on March 17, whilst unpopular, saved 2,200 jobs and a British company.
“P&O Ferries is now a modern, dynamic, competitive and viable business which can meet customer needs flexibly in a way that has not been possible in the past.
“We call on Government to have a constructive dialogue with P&O Ferries about the future and how we get this country moving in a positive direction after two very difficult years for business. Calls for our CEO to go need to stop.
“Despite the attempts from some parties to undermine our business by creating false rumours and uninformed commentary, our morale is high and our spirit as a company is strong.”
He added that P&O Ferries will “be back to full service shortly” and will “return to commercial viability soon”.
Mr Shapps told the committee that P&O Ferries should repay the £11 million of furlough money it claimed from the Government during the coronavirus pandemic.
He added that the company “will have to pay the minimum wage” when new legislation is introduced.
The new crew are being paid an average of £5.50 per hour.
This is below the UK’s minimum wage of £9.50 per hour, but P&O Ferries insists it is in line with international maritime law.
Mr Shapps said UK ports will be required to check with ferry operators that their crews are being paid at least the national minimum wage.
P&O Ferries resumed cross-Channel sailings on Tuesday night for the first time since the mass sackings.
The vessel Spirit Of Britain began operating between Dover and Calais for freight customers.
Passenger services are expected to resume early next week.
Spirit Of Britain was detained by the Maritime and Coastguard Agency (MCA) on April 12 after safety issues were found, but was cleared to sail on Friday.
Another P&O Ferries ship, European Causeway, was adrift five miles off the coast of Northern Ireland for more than an hour on Tuesday afternoon after losing power due to a mechanical failure.
The firm said it had been a temporary issue and the vessel reached Larne “under its own propulsion”.
An inspection is being carried out by the MCA.