US law enforcement officials became so concerned by President Donald Trump's behaviour in the days after he fired FBI Director James Comey that they began investigating whether he had been working for Russia against US interests, The New York Times has reported.

The report cites unnamed former law enforcement officials and others familiar with the investigation.

The inquiry forced counterintelligence investigators to evaluate whether Mr Trump was a potential threat to national security, and they also sought to determine whether Mr Trump was deliberately working for Russia or had unintentionally been influenced by Moscow, according to the report.

The Times reports that FBI agents and some top officials became suspicious of Mr Trump's ties to Russia during the 2016 presidential campaign but did not launch an investigation at that time because they were not sure how to approach such a sensitive and important probe, according to the sources.

But Mr Trump's behaviour in the days around Mr Comey's May 2017 firing, specifically two instances in which he seemed to tie Mr Comey's ousting to the Russia investigation, helped trigger the counterintelligence part of the investigation, according to the Times' sources.

Robert Mueller took over the investigation when he was appointed special counsel soon after Mr Comey's firing.

The overall investigation is looking into Russian election interference and whether Mr Trump's campaign coordinated with the Russians.

The Times says it is unclear whether Mr Mueller is still pursuing the counterintelligence angle.

Mr Trump's lawyer Rudy Giuliani told the Times that he had no knowledge of the inquiry but said that since it was opened a year and a half ago and they had not heard anything, apparently "they found nothing".

Mr Trump has also repeatedly and vociferously denied collusion with the Russians.

PA Media