Last week, more than 200 migrants, mostly from Eritrea and Somalia, died just a kilometre from the shores of the Sicilian island of Lampedusa when their boat caught fire and sank.
Malmström is due to visit Lampedusa on Wednesday, along with commission president José Manuel Barroso and deputy prime minister of Italy Angelino Alfano, in the spirit of European support.
Speaking at a press conference on Tuesday, the commissioner said, "The recent events are a European tragedy and concern all member states. This is why we have to act at European level to show concrete solidarity both with migrants and with countries confronted with extreme migratory pressure.
"Member states have to do more to help refugees and asylum seekers. These people are the most vulnerable and they have already gone through horrible events. It is unacceptable that they have to risk their lives in order to receive protection."
She continued, "Member states have to be more active in resettling refugees to the EU, in order to prevent these deadly crossings.
"Let's make sure that what happened in Lampedusa will be a wakeup call to increase solidarity and mutual support and to prevent similar tragedies in the future" - Cecilia Malmström
The commissioner also announced that she has proposed the deployment of an "extensive Frontex search and rescue operation that will cover the Mediterranean from Cyprus to Spain".
The Swedish official said "such an operation will help lead to quicker tracking, identifying and the rescuing of more vessels and boats, and therefore prevent the loss of lives at sea".
"I have made it clear to all ministers that these are European issues that require European answers. If they want to provide answers and show concrete solidarity they have to give the commission the appropriate financial resources.
"I am confident that today all member states have heard our strong call and will react accordingly.
"In the longer term we need a more open approach to migration, to define a common European policy based on the rights of the migrants and of the asylum seekers and on solidarity to both the migrants and the member states.
"Let's make sure that what happened in Lampedusa will be a wakeup call to increase solidarity and mutual support and to prevent similar tragedies in the future," she concluded.
In response to the incident Timothy Kirkhope, parliament's ECR group spokesman on justice and home affairs, said, "This has been a real tragedy, and unfortunately, these events have taught us lessons which we have learnt too late."
Speaking about the Frontex proposals, the British deputy said, "I have always been a supporter of Frontex, and supported calls for the agency to play a greater role in guarding the European borders including at sea.
"It is important not just for security and to combat smugglers and human traffickers who target Europe, but also in dealing with potentially fatal humanitarian problems.
"This new-found resolve is encouraging. It is something which I and the parliament have been calling for," he added.
"What we need now is for member states and the EU council to get behind these proposals, because too often in the past similar proposals have been shelved.
"This isn't about facilitating immigration, but about identifying those whose lives are at real risk and policing Europe's borders, so that we never have to witness events like this again," he urged.
ALDE leader Guy Verhofstadt expressed regret about the Lampedusa tragedy saying that it "could have been prevented".
He said that, according to the international maritime organisation, "25,000 migrants have lost their lives in the Mediterranean over the past 20 years."
"The issue of managing migration flows is complex but there can be no excuse for turning our backs on desperate asylum seekers at our borders," he continued, adding, "It is no good just wringing our hands at the plight of refugees and playing the blame game. Europe, together, must take collective responsibility."
The Belgian MEP, turning his attention to Frontex, said that the agency had "seen its budget cut from €115m in 2011 to €85m this year", and that "this is no way to run an effective border surveillance service or asylum assistance programme".
"We desperately need a common European migration policy. The legislative pieces are in place but member states have still to agree," he concluded.
Meanwhile, S&D group chair Hannes Swoboda said the matter of refugees crossing EU borders is "an EU competence, jointly with member states".
"We must help countries of origin so that the conditions which force people to leave are improved" and "we must give more support to transit countries like Tunisia and Lebanon which are faced with such high numbers of refugees," insisted the Austrian deputy.
"Promises of support are not enough; we must help them financially and ensure that the EU budget provides for such financial assistance," he concluded.
UK Green group member Jean Lambert criticised the response to the recent Lampedusa tragedy, saying, "Despite the outpouring of rhetoric from ministers and bigger political groups in response to the latest tragedy in Lampedusa, concrete proposals remain absent.
"EU governments and politicians have consistently blocked attempts to ensure EU border policies can focus on saving lives at sea and deciding which countries take responsibility for those saved: they have also failed to ensure that those seeking refuge can access asylum systems safely," she argued, before adding, "Therefore, it is hard to take such rhetoric at face value."