Before the attack, the teenager wrote a Facebook post announcing that the "time has come for a great revolt", as he condemned the Israeli crackdown on Palestinians in the Gaza Strip and the West Bank.
The Israeli army also said it is "reinforcing the defence" in the settlement of Adam, but Mr Lieberman suggested a longer-term strategy was needed.
The dead terrorist was identified as Mohammed Tarik Youssef, 17, from the Palestinian village of Kobar near Ramallah. The Israeli army said on Friday it had raided the village, questioned a number of his family members and suspended their work permits.
Palestinian militant group Hamas said the attack was an act of heroism and revenge for "crimes conducted by the Israeli occupation against our people".
He said he saw 31-year-old Yotam Ovadia "covered in blood ... walking slowly toward a vehicle and then falling".
The Israeli army said it responded to a Hamas sniper who opened fire on soldiers on the Gaza border.
Hamas' armed wing, the al-Qassam Brigades, said earlier Thursday that Israel "must pay a high price with its blood" making an apparent reference to the three killed Palestinians.
Hamas and the PFLP (Popular Front for the Liberation of Palestine) praised the "heroic" stabbing attack on Thursday.
Lone Palestinian attackers have carried out multiple deadly stabbings and car-rammings against Israelis in recent years.
More than 600,000 Jews live in about 140 settlements built since Israel's 1967 occupation of the West Bank and East Jerusalem.
Tensions have spiked since Palestinians began protesting along the Gaza border in late March, with Israeli fire killing at least 153 Palestinians since then.
Kevin Durant: LeBron James to the Lakers a 'Perfect Move'
I would choke up and wouldn't play my game and I'm still getting the hang of it.it's all a journey ... this kid has it all! "Anybody [who] starts judging a lot of players, me mainly, doesn't figure out that guys like me and Nick Young and J.R.