Writing in his regular blog Bildt said he was greatly concerned about the escalating violence in the Middle East. Last week he called for an 'immediate' ceasefire in the region and in his latest post said he believes Israel wants something similar.
"Israel has this time shown an openness to proposals regarding a ceasefire but thus far these have been consistently rejected by Hamas," Bildt wrote.
The former prime minister said the situation is similar to the violence in the region in 2008 - 2009 and also in 2012. He questioned what both Israel and Hamas were really managing to achieve in the conflict which has claimed more than 600 lives.
He added that the Israel blockade of Gaza should stop whilst also calling on Hamas to cease launching rocket attacks across the border in exchange for the blockade being lifted.
"From our side it is obvious that we are calling for an immediate ceasefire," he said.
Meanwhile, Social Democrat leader Stefan Löfven has criticized Israel for its actions in Gaza. Last week the election favourite sparked controversy when he wrote on Facebook that Israel had the right to defend itself.
"We are clear: this time it isn't a proportionate force. Israel is the stronger party," Löfven told Aftonbladet.
In a statement published on the Social Democrats' website Löfven went further describing the attacks on Gaza as "brutal" and "violent" whilst calling on Israel to comply with international law.
Löfven called on both sides to stop attacking each other and negotiate a ceasefire. He stated that he stood by his controversial Facebook post which generated thousands of negative comments about his stance.
"I stand by what I said then," he said.
Political scientist Stig-Björn Ljunggren told Aftonbladet that Löfven's latest statement was similar to what he had said before, except that he had chosen his words more carefully this time.
"Here they sat and looked at every single comma," he said.
Story continues below…
BBC news reported that 600 Palestinians and 29 Israelis have died since the conflict began a fortnight ago.
Attempts to negotiate a ceasefire are under way with US Secretary of State John Kerry due to discuss the matter with UN Secretary General Ban Ki-moon in Cairo.
Carl Bildt added in his blog that he would be speaking about the Gaza crisis at large during an EU foreign affairs meeting on Tuesday.