The Home Office and Ministry of Defence have been warned about the amount of time they are taking to answer Freedom of Information (FOI) requests.
The two departments are among 30 public bodies to be have been told to "get their houses in order" over the issue by the Information Commissioner.
The watchdog can take action if organisations fail to respond to requests within 20 working days.
Officials said all departments were "committed" to complying with FOI laws.
The Cabinet Office, which is spearheading the coalition's drive to make central government more transparent, is among the departments whose processes are under review by the watchdog.
The Department of Work and Pensions, The Scottish Office, the Northern Ireland Office, the Metropolitan Police, Transport for London and a number of county, district and borough councils are also being monitored after failing to respond to FOI requests on time.
'Taking it seriously'
Under FOI legislation which came into force in 2005, public organisations are required to respond to requests within 20 days or explain why it will take longer to do so.
The watchdog said the organisations under review had either failed to meet this deadline by a "significant margin" on several occasions or had been the subject of at least six complaints within a six-month period about their processes.
"We will monitor the authorities named for three months but may take action during this time frame if an authority's standard of compliance is revealed to be particularly poor or if it is unwilling to make the improvements necessary," said its deputy commissioner Graham Smith.
"This is a perfect opportunity for the authorities named to get their houses in order and demonstrate that they take Freedom of Information requests seriously."
The watchdog, which seeks to promote open government and a culture of maximum disclosure, has a range of powers at its disposal to deal with non-compliance.
In the most serious cases, where deadlines are repeatedly missed, requests turned down or details exempted without good cause, organisations can be served with an enforcement notice requiring remedial action within a certain period.
The only time this has happened was earlier this year when the Independent Police Complaints Commission was censured.
The Ministry of Justice, which oversees the government's FOI policy, said the right of individuals to access publicly-held information and hold government to account was "fundamental".
"Every Whitehall department is firmly committed to this principle," a spokeswoman said.
"We welcome the work the Information Commissioner has done to identify areas where improvement is required and support his efforts to improve compliance with the act.
"We will be working with the government departments in this list to help them improve their performance where needed."
Ministers were looking to extend the scope of FOI legislation to make government decision-making more transparent whilst protecting sensitive information, she added.