When Hamas came to power in 2006 after a fair election, as confirmed by the UN and US, they repeatedly sent peace feelers to the Israeli government. This implied they were seeking some form of settlement and peaceful coexistence with Israelis. However, the Israeli government dismissed all these efforts. Although a ceasefire was later reached, it was soon broken unilaterally by Israel.

While it's true that Hamas at the time of sending peace feelers asked for the right of return for all refugees expelled from their homes in 1948—a demand not favored by Israel—one should note that, first, international law does recognize the right of return for expelled people, and second, Hamas presented it as a topic of negotiation, which Israel refused to engage in.

When Hamas, the most hardline Palestinian group, pursued peaceful coexistence with Israel, other Palestinian groups would have naturally followed, debunking the Israeli claim that Palestinians are a constant source of insecurity for Israelis.