Internal Security Minister Avi Dichter offered a surprisingly optimistic view Monday of prospects for peace between Israelis and Palestinians, despite what he called a big push by Iran to sow discord in the region. "I spent more years in Gaza than I spent in Tel Aviv. I think I know them (the Palestinians) very well," Dichter told a gathering of diplomats and reporters in Jerusalem. "So the probability that I see, the probability to set up a peace agreement and a peace situation ... is much stronger than the probability that we are going to get into another round of violence." Asked to explain why he was so upbeat, Dichter - who headed the Shin Bet (Isreal Security Service) during the IDF's crackdowns on Palestinian terrorists - predicted Palestinians would ultimately understand they have no choice but to accept Israel. "They know that they have no chance to build themselves as a nation without a peace agreement with Israel," he said. Dichter accompanied his upbeat view about peacemaking with an account of the grave dangers posed by Iran, which he said is waging two simultaneous proxy wars against Israel in both the north and south - through Hizbullah guerrillas in Lebanon and Hamas operatives in the Gaza Strip. Still, Dichter said he believed that the 34-day war in Lebanon last summer would make Hizbullah think twice before launching new attacks. "I believe that the level of deterrence that Israel created toward Hizbullah is probably the main positive issue that we have gained from the last war in Lebanon," he said. Dichter accused Iran of training Hamas gunmen from Gaza who took advantage of an opening of the Gaza-Egypt border following the disengage in 2005. He called Hamas's exiled supreme leader, Khaled Mashaal, a "frequent flyer between Damascus and Teheran" and said the group was building a sophisticated arsenal of smuggled weaponry in Gaza. Offering another reason why peace is not out of the question, Dichter said there was a difference in the outlook between Hamas in Gaza and its exiled leadership in Syria. "The external leadership of Hamas in Damascus is much more extremist than the leadership in the Gaza Strip because as we all understand, those who count the lashes are not like those who are suffering it," he said, referring to the impact of Israeli retaliatory strikes that follow Palestinian violence.