The United States has said its recent actions against Syrian government forces and allied militia have been self-defensive in nature, aimed at stopping attacks on US -led coalition forces or their local allies.
Yaari also told The Times of Israel that his sources were "amazed" at the poor performance of the Iranian missiles.
Lt. Gen. Gadi Eizenkot said Tuesday the "operational achievement was much smaller" than what has been reported.
Israel and Iran are bitter enemies.
Iran launched the missiles into Syria on Sunday, the first time in 30 years it has used them against a foreign country.
The attack last week, which included shootings and at least one suicide bombing, was on Iran's parliament and the shrine of Ayatollah Khomeini, the founder of the Islamic Republic.
Elsewhere, the US military confirmed Tuesday that top ISIS cleric Turki al-Binali was killed in a coalition airstrike May 31 in Mayadeen, Syria.
State television said the attack killed an IS commander, a Saudi national named Saad al-Hosseini, known as Abu Saad. The Bahraini cleric wrote religious justifications for the enslavement of hundreds of women from Iraq's Yazidi minority and helped establish the IS branch in Libya. He rose to be one of the extremist group's leading ideologues.
A Syrian military official in Damascus said the truce was not extended. Iran claimed that multiple Islamic State members were killed in the attacks and that parts of a weapons depot were destroyed. USA -backed forces recently pushed into Raqqa, the northern Syrian city that served as the group's de facto capital.
The White House has not commented on Iran's missile attacks inside Syria.
"The Obama administration constantly spun journalists on foreign policy, and that created this idea that if officials aren't talking about something, they're not paying attention", said the source, a veteran foreign policy adviser who is in routine contact with the White House.
The incidents reflect mounting competition for areas of Syria where Islamic State (IS) insurgents are in retreat, leaving swathes of territory up for grabs and posing the question of what comes next for US policy that is shaped first and foremost by the priority of vanquishing the jihadists.
This month, an American F-15E shot down an Iranian-made drone after it attacked American fighters in southeastern Syria. He spoke on condition of anonymity in line with regulations. Coalition aircraft stopped the pro-regime forces from advancing on Ja'Din. A U.S. Super Hornet immediately responded and shot down the Syrian plane.
"The Syrian regime ... needs to understand that we will keep the right of self-defense of coalition forces aligned against ISIS", he said. ISIS forces now surround an estimated 200,000 people in the province, which is held by the Syrian government. The truce was meant to be extended but now appears to have collapsed.
"The situation is back as it was in Daraa city and fighting is ongoing", said Daraa-based opposition activist Ahmad al-Masalmeh. He is blaming the government for the truce's collapse.
Late Sunday, the elite Revolutionary Guards launched six missiles from western Iran into Syria's mostly Islamic State group-held Deir Ezzor province, hitting an IS command base, the Guards said.
Sunday's strike came amid rising tensions between Riyadh and Tehran.
It was not known what exactly was hit and Iran has provided no details.
"The Coalition has made it clear to all parties publicly and through the de-confliction line with Russian forces that the demonstrated hostile intent and actions of pro-regime forces toward Coalition and partner forces in Syria conducting legitimate counter-ISIS operations will not be tolerated", USA military officials said.
"We have agreed in the past, that is we and the Russian Federation pro-regime forces, that operations that the coalition were conducting in Syria were effectively degrading ISIS capability, and will work to restore that de-confliction chain in the next few hours", Dunford said.
"I hope that the clear message of this attack will be understood by the terrorists as well as their regional and worldwide supporters", said Amir Ali Hajizadeh, the head of the Revolutionary Guards' aerospace unit, according to the website of Iranian state television.
Deir el-Zour is home to both Islamic State militants and civilians.
Russia's Defence Ministry said yesterday it would view as targets any flying objects over Syria in areas of the country where its air forces operate.
The development comes as tensions rise in Syria with Russian Federation and Iran sending USA warnings.
The president also put Tehran "on notice" in February after it launched a ballistic missile.