Jerusalem (CNN) As politicians in Israel raced to alleviate concerns over US President Donald Trump's alleged disclosure of classified Israeli information to the Russians, the country's former top spy has warned of the damage the episode could do to US-Israeli intelligence sharing and to Israel's ability to gather information on ISIS.

Israeli intelligence was a source for some of the highly sensitive information about the terror group's bomb-making capabilities that the President discussed with Russian diplomats at the Oval Office last week, US and diplomatic officials told CNN on Tuesday.

Danny Yatom, who led Israel's secretive Mossad agency from 1996-1998, warned of a "very bad development" and a possible "catastrophe" if Trump compromised an Israeli source during the White House meeting.

"If we will assess that our sources of intelligence are in danger due to the way it will be handled by the United States, then we will have to keep the very sensitive information close to our chests," Yatom told CNN.

The revelation may be a significant blow to Israel's ability to collect intelligence about ISIS, Yatom warned.

"I hate to reiterate it, but it might cause a dramatic change to our capabilities to continue and to collect vital information on ISIS," he said. "The enemy can very easily identify and recognize where the information came from and start searching for collaborators."

Israel and the US would not publicly comment on claims Israel was the source of the intel. But the White House has insisted that Trump did not risk national security by sharing information with top Russian officials and revealed that the President did not even know the source of the intelligence he divulged.

Fallout: Far-reaching or flash in a pan?

Trump and Netanyahu shake hands during a joint news conference at the White House in February.

Israeli Prime Minister Benjamin Netanyahu spoke with Trump over the phone on Tuesday night, but the Prime Minister's Office says Trump's upcoming visit to the region was the only topic of conversation. Netanyahu has not commented on the disclosure of information to the Russians.

Israeli Defense Minister Avigdor Liberman insisted there would be no effect on the close relations between the United States and Israel. "The security relationship between Israel and our greatest ally the United Sates, is deep, significant and unprecedented in volume," he tweeted Wednesday. "This is how it has been and how it will continue to be."

Transportation Minister Yisrael Katz echoed that message in a statement. "Intelligence cooperation between Israel and the United States regarding the threats posed by Iran and its proxies and ISIS and its affiliates will continue and deepen," he said.

But it may be too early to know the lasting consequences of the information Trump revealed to the Russians.

"We don't know what kind of information was transferred, we don't know what sensitivity this information carries and if it can reflect about the source that gave us the information," said Brig. Gen. (ret.) Amnon Sofrin, who is the former head of the Mossad Intelligence Directorate. Sofrin warned the fallout could be far-reaching.

"If this really happened and there is some reflection about the source, it may cause very big trouble for us, because it can put into risk the source and may cause some damage to our activities," Sofrin told CNN.

Even so, Sofrin described the conversation between Trump and the Russians as a small event, and said it would not imperil the relationship between the Israeli and American intelligence communities.

"The cooperation between the two organizations is so solid that such an event cannot cause any big damage. It may cause small damage, but not a disaster."

The unwritten rule in intelligence-sharing

Intelligence sharing between allies -- in particular those as close as Israel and the US -- is standard practice. But Sofrin points to an unwritten rule between intelligence agencies: sensitive information will not be shared with other countries without explicit permission, and the way in which that information is shared will reflect its sensitivity.

In defending Trump's disclosure of the information, National Security Advisor H.R. McMaster appeared to acknowledge Tuesday that those protocols had not been followed. "I should just make the statement here that the President wasn't even aware of where the information came from," he said. "He wasn't briefed on the source or method of the information either."

Uzi Arad, the former head of Israel's National Security Council under Netanyahu, said the revelation will not affect the close relationship between the two countries' intelligence communities. "This will not affect the policy or the sharing of intelligence with the United States, and we will continue to work very closely with the American intelligence community," Arad said.

Despite Russia's years-long standoff with many countries in the West, Israel maintains a strong relationship with the Kremlin, as evidenced by Netanyahu and Liberman's recent visits to Moscow.

The two countries also maintain an open line for security coordination, especially in the airspace above Syria. But Russia's alliance with Syrian President Bashar al-Assad, which has close ties to Iran -- and by proxy, the Lebanese militant group Hezbollah -- means Israel must be careful with its intelligence.

This caution specifically applies to intelligence about ISIS, where Arad says there is no security coordination with the Russians.

Arad points out that not sharing classified information, especially with an ally as close as the United States, is not feasible.

"The only other option is not to say anything, but that can lead to even greater harm [to Israeli interests]," Arad said. "Leaders must be able to weigh the benefits and costs when speaking with other leaders."

The concern is that Trump never made that calculation.