High Representative of the European Union for Foreign Affairs and Security Policy Kaja Kallas. AFP
The most intense escalation since a November ceasefire, which ended the war between Israel and the Iran-backed militant group Hezbollah in Lebanon, occurred on Saturday.
Lebanon's health ministry said eight people have been killed in the flare-up.
Despite the ceasefire, Israel has continued to carry out strikes on Lebanon.
"Military actions must be proportionate, and Israeli strikes into Syria and Lebanon risk further escalation," Kallas said at a joint news conference with Israeli Foreign Minister Gideon Saar.
In Syria, Israel has launched hundreds of strikes on military sites since Islamist-led rebels overthrew strongman Bashar al-Assad in December. Israel says it wants to prevent weapons from falling into the hands of the new authorities it considers jihadists.
"We feel that these things are unnecessary because Syria is right now not attacking Israel and that feeds more radicalisation that is also against Israel, which we don't want to see," Kallas told journalists.
The Israeli military has also deployed to the UN-patrolled buffer zone on the Golan Heights, separating the Israeli-occupied part of the Golan from that still controlled by Syria.
Israeli Prime Minister Benjamin Netanyahu has demanded the demilitarisation of southern Syria and said his country will not tolerate the presence of forces from the new authorities south of Damascus.
Syria's foreign ministry has accused Israel of waging a campaign against "the stability of the country".
Gaza governance
When asked about Israel's stance towards Syria's new leaders, Kallas said: "Of course our worries are the same. They say the right things, will they do the right things?"
"But we have discussed this in the European Union and amongst all the member states, and our view is that we need a stable Syria," she added.
Kallas also spoke on war-ravaged Gaza, where Israel restarted intense air strikes last week followed by ground operations, shattering the relative calm of a six-week ceasefire agreement with Hamas.
The health ministry in Gaza said Monday that 730 people had been killed since Israel resumed bombardments on March 18, including 57 in the past 24 hours.
"The fundamental steps here are restating the ceasefire, ensuring the release of all hostages, and resuming the flow of humanitarian aid into Gaza with the goal of a permanent ceasefire," the EU's top diplomat said.
"The European Union can help, whether through restating our Rafah border-crossing mission or providing more humanitarian assistance," she added.
Kallas, who visited Egypt on Sunday, said the EU welcomed the Arab plan for reconstructing Gaza but that more needed to be done on issues such as cost-sharing and the future of governance.
"We see no role for Hamas in the future governance of Gaza," the diplomat said.
"We need to discuss how the governance of Gaza is foreseen... and the European Union is ready to participate in those discussions," she added.
Kallas is due to hold talks with Palestinian Prime Minister Mohammad Mustafa in the occupied West Bank later on Monday.
Short link: