Both Prime Minister Binyamin (Benjamin) Netanyahu and President Mahmoud Abbas need to do whatever they can to rein in this latest round of extremism displayed on both sides, but it's important to note that President Abbas has little influence on Palestinian extremists. Many Palestinians have become drawn to the extremists due in part to the collapse of the peace talks. They're disillusioned by being stymied and humiliated at the peace talks, and by Israeli announcements of further settlement construction.
On the other hand, Prime Minister Netanyahu really needs to show he means business by cracking down on Israeli extremists, extolling them on the fact that there can be no one-state solution. He can also put out the order to remove all settlements so that the peace talks can resume. The problem is that this will not happen if Prime Minister Netanyahu remains in office. He's shown time and again that he's not interested in peace.
If another intifada does spring up, it will be the Israeli side that caused it by attempting to hijack the talks and railroad the Palestinians into submission. It's a failed strategy with deadly consequences.