Other Swedes joining the call for action were Gunilla Carlsson, a former International Development Minister and Swedish businesswoman Karin Forseke, Alliance Trust, an investment and savings business.
"Migration is a complex problem that needs a comprehensive and long-term approach, but the first priority for European leaders must be to stop the death toll that is a stain on the conscience of our continent," said the statement, published on the European Council on Foreign Relations website.
— Carl Bildt (@carlbildt) April 23, 2015
"We call on the EU Heads of State and Government to go beyond the ten-point plan issued earlier this week in immediately restoring an expansive search and rescue operation in Mediterranean waters, with a mandate and level of funding that match the humanitarian emergency that confronts us."
The statement added that the EU must accept that attempts at migration will continue on a large scale and develop a range of measures that reflect our values and responsibilities."
READ ALSO: 'Swedes will compare this to the Holocaust'
The group called for restoring and expanding search and rescue operations; setting up a system of relocation for migrants throughout the EU; promoting and funding refugee facilities outside the EU; increasing quotas and creating a cooperative law enforcement team to break up trafficking networks.
Others who signed the statement included Dutch Princess Mabel of Orange-Nassau, former Italian prime minister Massimo D'Alema and Hungarian-American billionaire business magnate George Soros.
The statement came on the heels of a meeting of European leaders in Brussels on Thursday to discuss new strategies in the wake of the latest disaster on Sunday, in which hundreds of migrants drowned when their boat capsized on the way from Libya to Italy.
A confidential draft for the Brussels meeting obtained by the Guardian revealed that most migrants attempting to reach Europe via the Mediterranean would be sent back through a new rapid-return programme under the EU border agency Frontex.
The Guardian also reported that a major increase in search-and-rescue operations on the Mediterranean would likely not occur, according to the draft, despite pressure to do so.
Frontex director Klaus Rösler was hit by a protester with a bag of jam on Wednesday during a demonstration against the EU's refugee policy.
Soon after news broke of the most recent tragedy on Sunday, Spanish Prime Minister Mariano Rajoy called on the EU to do more to prevent more loss, saying "words alone are not enough" and promising Spain would continue to pressure the EU to handle migration better.
Swedish MEP Cecilia Wikström has also been among the most vocal campaigners on the issue and told The Local this week that ignoring the crisis was akin to turning a blind eye to the Holocaust.
An initial EU ministerial meeting on Monday called for a "civil-military" response to the crisis in the Mediterranean, and British Prime Minister David Cameron is reportedly considering the deployment of one of the country's biggest warships in a bid to "go after the criminal gangs".
Experts have warned, however, that tackling the problem militarily is doomed to fail.