“Everyone realises… that if the discussions fail the situation in the region will most probably worsen dramatically,” Bildt, who is in the United States to attend the Middle East peace summit beginning in Annapolis on Tuesday, wrote in the Dagens Nyheter daily.
“It is unfortunately easy to see that president Abbas will then disappear from the Palestinian side, and in his place more militant forces will most probably take over,” he added.
Sweden is one of about 40 countries attending the summit, the first major push for peace in the Middle East in seven years.
Major differences remain between the Israelis and Palestinians over core issues like the status of Jerusalem, which both sides claim as their capital, the borders of a future Palestinian state and the fate of Palestinian refugees.
Bildt warned that the summit could be “the last real chance to achieve a true two-state solution.”
He insisted however that “there is a certain responsibility to be optimistic. It is not through continuous pessimism that the world will change for the better, but only through actually trying to do what everyone realises must be done.”