Two Iranian warships have crossed the Suez canal en route to Syria, in a move that Israel said it viewed with the "utmost gravity".

The naval frigate and a supply ship entered the canal at 5.45am after receiving approval from the Egyptian authorities. It was the first time Iranian naval vessels have passed through the strategically important waterway since before the fall of the Shah of Iran in 1979.

There was no immediate reaction from the Israeli government, but the prime minister, Binyamin Netanyahu, told his cabinet on Sunday that Iran was trying to exploit instability across the region.

"I think that today, we can see what an unstable region we live in, a region in which Iran tries to exploit the situation that has been created in order to expand its influence by passing warships through the Suez canal," he said.

"Israel views this Iranian move with utmost gravity and this step, like other steps and developments, underscores what I have reiterated in recent years – Israel's security needs will grow and the defence budget must grow accordingly."

Last week, Israel's foreign minister, Avigdor Lieberman, described the Iranian move as a "provocation that proves that the self-confidence and impudence of the Iranians is growing from day to day ... Regrettably the international community shows no willingness to deal with these repeated Iranian provocations." Israel, he said, could not ignore such provocations forever.

The ships took about 10 hours to complete the 120-mile passage from the Red Sea to the Mediterranean. They will pass along Israel's coast on their way to take part in a training exercise with Iran's close ally Syria.

Israel is deeply concerned about the implications of mounting unrest across the Middle East and fears the fall of the former Egyptian president Hosni Mubarak could jeopardise the 31-year-old peace treaty between the two countries.

"The peace treaty [between Israel and Egypt] was the most important factor for stability in the Middle East – and stability is the key thing," said Ilan Mizrahi, a former head of Israel's national security council. Egypt, he said, "in the short term will be another point of instability" alongside Iran, Lebanon and Gaza.

Israel is also alarmed that the tumult sweeping the Arab world and Middle East has diverted international attention away from diplomatic efforts to halt Iran's nuclear programme.

Under international law, only ships from countries at war with Egypt are barred from passing through the Suez canal. But military ships need prior permission from Egypt's defence and foreign ministries.