The government insists only a fraction of the electronic communications will be affected, but critics worry the program, designed to combat terrorism and other threats to national security, is too far-reaching.
Their concerns resemble criticism of a U.S. surveillance program launched in 2001 that monitors international phone calls and E-mails to or from the United States involving people suspected by the government of having terrorist links.
The Swedish proposal, which needs parliamentary approval, would give the National Defense Radio Establishment a green-light to use so-called data mining software to search for sensitive keywords in all phone and e-mail communication passing through cables or wires across the country's borders.
Today, such traffic can only be monitored with court approval if police suspect a crime, although the agency is already free to spy on airborne signals, such as radio and satellite traffic.
European governments have gradually been expanding their surveillance powers, wiretapping rules and police search powers as part of efforts to unravel terror plots. But the Swedish proposal is among the most far-reaching when it comes to intercepting e-mail traffic.
The Dutch secret service can monitor E-mail in specific cases, but does not have a mandate to conduct blanket monitoring of international traffic.
In Britain, E-mails can only be intercepted with a warrant signed by a secretary of state, and the intercepted communications cannot be used in court.
Sweden's center-right government says it's only interested in international traffic, and that E-mails and phone calls between Swedes will be filtered out.
"This is about mapping situations so that we in Sweden will be able to fulfill what is one of the most central tasks for a government: protecting the country and its own citizens," Defense Minister Mikael Odenberg said.
However, critics say it is impossible to make such guarantees, as E-mails sent between two colleagues in the same office are often routed via a server abroad and could end up in the military's hands.
"They're going from fishing with a hook to fishing with a net," said Par Strom, a spokesman for The New Welfare Foundation, a civil liberties think tank. "We are crossing a very fundamental border."
Even Sweden's security police, SAPO, has criticized the proposal, saying it violates personal integrity.
Opposition politicians from the Green and Left parties say they will fight the bill when it comes to a vote in Parliament later this year. The main opposition Social Democrats said they had not yet decided how to vote.
"We're going to evaluate whether there are enough guarantees to safeguard people's integrity," said Thomas Bodstrom, justice minister in the previous Social Democratic government. "The other issue is, do we want to change society so that the military gets a completely new role when it comes to fighting crime?"