Johnson's office had no additional comment on Saturday.
Cummings said he will answer questions about any of the issues he has raised when he appears before lawmakers on May 26. The combined death toll is now more than 127,000, one of the highest in Europe.
Simon Case, the Cabinet Secretary, is expected to say his inquiry into the leak last autumn is still "live" when he appears before the Commons Public Administration and Constitutional Affairs Committee (PACAC).
Labour has also called for a new independent commission to be launched, on ethics and standards in government.
Ministers have denied claims that Boris Johnson was prepared to let "bodies pile high" rather than order another coronavirus lockdown, as the fallout from Downing Street's bitter briefing war continued. Opposition parties have picked up on the allegations ahead of local elections next month.More news: Caitlyn Jenner Is Officially Running for Governor of California
The disclosure is likely to further anger Mr Cummings, who released his onslaught after he was accused by No 10 of a series of damaging leaks, including text message exchanges between Mr Johnson and the entrepreneur Sir James Dyson.
Cummings said Johnson's plans to have donors secretly pay for the renovation of his Downing Street plan were "unethical, foolish, possibly illegal and nearly certainly broke the rules on proper disclosure of political donations".
Asked about the allegations, Defence Secretary Ben Wallace said Mr Johnson had paid "out of his own pocket" for the Downing Street upgrade.
Dominic Cummings, special advisor for Britain's Prime Minister Boris Johnson, walks along Whitehall in London, Britain, September 10, 2020.
Cummings, architect of the Brexit campaign for Britain to leave the European Union, left Johnson's staff suddenly late last year having previously been his most influential adviser over Brexit and a 2019 election campaign.More news: National advisory committee recommends AstraZeneca vaccine for people 30 and older
His blog post capped a hard few days for Johnson, following the resignation of defense minister Johnny Mercer who told Times Radio the government was "the most distrustful, bad environment I've ever worked in".
Cummings, a key force behind the successful Brexit campaign, led by Johnson, was a close and powerful advisor to the Prime Minister until he was unceremoniously ousted last November. But it risks reviving memories of the lobbying scandals that plagued the Conservative government of the 1990s and helped usher in 13 years of Labour rule.
British newspapers said on Sunday that Johnson's current advisers were anxious that Cummings would make further damaging allegations when he speaks to parliament next month about the government's handling of the coronavirus pandemic.
In a statement, Johnson's Downing Street office said the prime minister had "never interfered" in the inquiry and that the government had "acted in accordance with the appropriate codes of conduct and electoral law" on issues involving the funding of the apartment refurbishment.
Labour Leader Keir Starmer latched onto the allegation to reiterate his call for an inquiry into the accusations that have dogged Johnson and his government for the past couple of weeks. Only the headline has been changed.More news: Russia: Doctors denied access to ‘very weak’ Alexei Navalny