"I think all countries that don't want to see Iran as a nuclear power should work together and probably adopt a new UN Security Council decision on sanctions," Anna Azari told journalists.
Azari said Israeli authorities believe that despite the Islamic Republic's refusal so far to halt uranium enrichment, sanctions do nevertheless have an influence on the country's leadership.
The United Nations Security Council has passed two rounds of sanctions against Iran over its nuclear program, which Western nations suspect is geared toward building atomic weapons, despite Tehran's denials. The United States and France have pushed for tougher sanctions, but Russia and China have blocked the measures.
"We believe all is not lost, and that we need to move forward using political and economic means," she said.
The 35-nation Board of Governors of the UN nuclear watchdog, the International Atomic Energy Agency (IAEA), will consider on Thursday and Friday Iran's cooperativeness with IAEA following a generally positive report earlier this month on Tehran's nuclear activities by head of the watchdog.
On the subject of Syria, Azari said Israel is interested in peaceful relations with the country, but that Tel Aviv is not sure whether the intent is mutual. "Israel is interested in peace with Syria and is ready for compromises," she said.
"Syria wants the Golan Heights, but we don't see that it is ready to demonstrate its drive for peace with Israel," she said, adding that Syria continues to supply radical movements with weapons.
Israel has stationed troops on the Golan Heights since seizing the territory from Syria in the 1967 Six-Day War, but the Israeli military recently announced a partial withdrawal due to the increasingly low threat of an armed conflict with Damascus.
Asked about Israel's concerns that Russian weapons being supplied to Syria could eventually end up in the hands of Lebanon-based Islamist group Hizbollah, the ambassador said the threat is genuine.
"No country welcomes arms deliveries to states it has no peace with. We know that Vladimir Putin is a friendly president toward Israel, and he has pledged not to change the strategic balance in the region. We think he will keep his promise," Azari said.