Bletchley Park, the home of British code-breaking during World War II, has called Number 10's refusal to provide it with additional funding "disappointing".
More than 20,000 people signed a public petition to the prime minister asking for £250,000 per year, for five years, to cover operational expenditure for the museum at Bletchley Park. On Thursday, the government declined to offer the funds.
Simon Greenish, director of Bletchley Park Trust, said on Friday that the sum to keep the museum running was insignificant, in comparison with the historical significance of the site.
"The support we are requesting from the government is modest," said Greenish in a statement. "It is the operational costs of running this large and ageing site that the trust struggles to meet."
The Downing Street petition closed in May with 21,920 signatures. The government rejection of it elicited expressions of support from hundreds of people, Bletchley Park said, including writer and actor Stephen Fry.
On Friday, Fry lent his support to Bletchley's continuing quest for operational funds. "If we can't save the place that arguably did the most to win us the war, what hope is there for us as a nation?" Fry was quoted as saying in Bletchley Park's statement.
The prime minister's office said while it recognised the historical significance of the code-breaking site, it had no plans to provide the requested funding.
"The government agrees that the buildings on the Bletchley Park site are of significant historic importance and, although recognising the excellent work being carried out there, at present it has no plans, nor the resources, to extend its sponsorship of museums and galleries beyond the present number," said the e-petition response.
Downing Street noted that Bletchley had secured funding from Milton Keynes Council and English Heritage, and was in the process of applying for a grant from the Heritage Lottery Fund. The government turned down a similar request for funds in May.