Wolfensohn acknowledged on Wednesday that it needed the intervention of US Secretary of State Condoleezza Rice to arrange an agreement on Tuesday for the reopening of the Gaza Strip's borders, which have been largely closed since Israel left the territory more than two months ago.
The Australian economist had been appointed by US President George Bush to help coordinate the economic aspects of the Gaza pullout, but he told Israeli public radio that his influence was not enough to bear fruit.
"If after 20 weeks, you cannot make up your mind on the same issue (the borders) that we were talking around for 20 weeks, there's probably not much more I can do," he said.
"The breakthrough came in the last couple of days, and I think one should give credit to (Rice) because she happened to be here, and she is a woman who has greater power and greater influence than I do.
"The United States has, as I think you know, a very strong influence on Israel and a pretty strong influence on the Palestinians, and you know they could, maybe, ignore me; but it's very difficult to ignore the secretary of state."
"If after 20 weeks, you cannot make up your mind on the same issue (the borders) that we were talking around for 20 weeks there's probably not much more I can do"
James Wolfensohn, international envoy to the Middle East
A clearly disillusioned Wolfensohn said he would consider his position and decide whether he felt he could still make a contribution to the peace process.
"I am just going to see in the next quarter of this year what my own plans are and see whether I can still make a contribution or maybe there will be others who can do better than me."