Asked whether Israel should be less wary of possible flare-ups on the Golan - much of which it seized from Syria in a 1967 war and annexed in a move not recognised overseas - Lieberman said: "I believe so".
The terrorists had crossed into Israeli territory but had not yet breached the security fence, Conricus said, indicating the terrorists may have been on the way to attack Israel.
The Israel Defense Forces said on Thursday it had targeted and killed seven "armed terror operatives" just 650 feet from the Israeli border on the Golan Heights.
Meanwhile, in a major change to the pre-conflict 2011 status quo, Russian military police began deploying on the Syrian-held Golan and planned to set up eight observation posts in the area, the Defence Ministry in Moscow said.
The military described it as a "triangle area" near the borders of Israel, Syria and Jordan in the occupied Golan Heights.
Syrian rebel fighters and government forces have clashed in the area, though President Bashar al-Assad has regained control of late.
Israel said the group was around 200m (656ft) from an Israeli fence in the zone, delineated by Israel and Syria in 1974. The UN mission was also unable to access a refugee camp in Israel via Syria. They didn't elaborate but later Putin said he agreed with Trump on securing Israel's border with Syria in line with the 1974 deal.
Israel's military spokesman, Lt. Col. Jonathan Conricus, said in a telephone briefing with reporters that he could not immediately comment on the United Nations deployment on the Syrian side of the border. An initial assessment by Israel's military identified the gunmen as Islamic State militants, in what would mark a rare attempt by the Islamist militants to infiltrate Israel.
A series of blistering offensives backed by Moscow and Tehran has forced the rebels out of many of their strongholds, putting Assad's government back in control of almost two-thirds of the country.
Hezbollah and other Iranian-backed Shiite militias reportedly played a key role in re-capturing the region along the border despite Russian assurances they would be kept away from the Israeli border and denials by the Assad regime the Iranian trained and funded forces were taking part in the battle.