US President Trump has hit back at reports he shared classified information with Russia's foreign minister at the White House, saying he had the "absolute right" to tell him what he did.

"As President I wanted to share with Russia (at an openly scheduled WH meeting) which I have the absolute right to do, facts pertaining ... to terrorism and airline flight safety," Trump said on Twitter on Tuesday.

"Humanitarian reasons, plus I want Russia to greatly step up their fight against ISIS & terrorism."

Today's pushback from Trump comes after a Washington Post report, later confirmed by other media outlets, said he jeopardised a critical intelligence source by disclosing information that had been regarded as highly secret, even inside the US government.

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Officials said the President told Russian foreign minister Sergei Lavrov details of the "inner workings" of Isis that could expose the source of the information - one of America's allies - and the methods used to obtain it.

According to AP, Trump boasted about his access to classified intelligence during the meeting with Lavrov. An excerpt from the official transcript of the meeting reveals Trump said: "I get great intel. I have people brief me on great intel every day."

Multiple media outlets, including CNN, the Wall Street Journal and the New York Times, are now reporting Israel was the source of the information. The US shares a "unique" intelligence-sharing arrangement with Israel - which could be damaged by Trump's actions.

"There is a special understanding of security cooperation between our countries. To know that this intelligence is shared with others, without our prior knowledge? That is, for us, our worst fears confirmed," an Israeli intelligence officer told Buzzfeed.

The officer went on to say they "would not trust a partner who shared intelligence" without telling them first. However Israel's ambassador to the United States, Ron Dermer, issued a statement to the New York Times reaffirming the countries' close relationship.

"Israel has full confidence in our intelligence-sharing relationship with the United States and looks forward to deepening that relationship in the years ahead under President Trump," Dermer said.

Meanwhile the White House, which had tried to hose down the story yesterday, has changed tactics. Now it says Trump's disclosure was "wholly appropriate".

National Security Adviser H.R. McMaster said the President engaged in "routine sharing of information" and nothing more.

"In the context of that discussion, what the president discussed with the foreign minister was wholly appropriate to that conversation and is consistent with the routine sharing of information between the president and any leaders with whom he is engaged."

Yesterday, McMaster denied the story outright.

"At no time were any intelligence sources or methods discussed and no military operations were disclosed that were not already known publicly," he said at the time. "The story that came out tonight, as reported, is false. I was in the room, it didn't happen."

As President, Trump has the power to disclose classified information as he chooses. Yet his decision to reveal an ally's information on ISIS with another country - and a geopolitical adversary, at that - could damage his standing with world leaders and lead some countries to start second-guessing their own intelligence-sharing agreements with the US.

"The story that came out tonight, as reported, is false. I was in the room, it didn't happen."

Today President Trump met with Turkish President Recep Tayyip Erdogan at the White House. They were expected to address the Syrian Civil War and the refugee crisis in a meeting complicated by regional politics in the Middle East.