By Alexis Flynn And Reed Albergotti 

LONDON--British intelligence agents should have done more to monitor two Islamic extremists who later killed a soldier on the streets of London, a panel of U.K. lawmakers concluded, in a report that also laid into U.S. Internet companies it said weren't doing enough to help fight terrorism.

The Intelligence and Security Committee reported its findings Tuesday after a yearlong investigation into what the intelligence services knew and whether they could have prevented the al-Qaeda-inspired murder of 25-year-old Lee Rigby as he returned to his barracks one afternoon in May 2013.

The panel concluded that British intelligence couldn't have stopped the attack. But it said that the killing might have been averted if an online exchange between one of the killers and an overseas extremist had been revealed to authorities by the internet company. While the committee didn't name the company, a person familiar with the matter identified it as Facebook Inc.

Zeroing in on an area of tension between Britain and overseas Internet firms, the committee's chairman, Malcolm Rifkind, said U.S. companies weren't proactively monitoring suspicious content and didn't feel obliged to comply with U.K. warrants, which he said was a "great concern."

Facebook said it doesn't comment on individual cases but the company's policies are clear. "We do not allow terrorist content on the site and take steps to prevent people from using our service for these purposes," the company said.

Mr. Rifkind also criticized the government's counterterror strategy more broadly, saying it was failing to prevent large numbers of people from leaving the U.K. to travel to Syria and Iraq and needed to do more to root out individuals before they embark on a process of radicalization.

The 200-page report provides a rare window into the workings of Britain's secretive intelligence agencies, which are monitoring several thousand individuals linked to Islamic extremist activities in the U.K. It also comes at a time when authorities in the U.K., the U.S. and elsewhere are warning of an increasing threat from so-called lone-wolf attacks, or self-radicalized terrorists.

The two attackers, Michael Adebolajo and Michael Adebowale--both British citizens of Nigerian descent and Muslim converts-- were convicted of murder in 2013 and sentenced to life imprisonment this year.

They drove a car at high speed into Mr. Rigby as he crossed the street. After the car crashed into a lamppost, the two attackers exited the car and began to hack at Mr. Rigby with knives before dragging his body into the middle of the road.

Prior to the attack, the two men had appeared in seven different intelligence investigations, according to the report.

Mr. Adebolajo, who had been arrested by Kenyan police on suspicion of fostering links with Somali militant group al-Shabaab and deported back to the U.K., was a high priority for MI5 during two operations when significant effort was made to investigate him. But these investigations didn't reveal any evidence of attack planning, according to the report.

Mr. Adebowale was never more than a low-level interest to the authorities. While they were ramping up their investigation of him, MI5 hadn't received any intelligence that he was planning an attack, the report found.

Still, the committee found there had been errors in these operations, such as delays. One important delay occurred in the submission of an application to use further "intrusive" investigative methods against Mr. Adebowale. Had the application been processed more swiftly, the domestic intelligence agency, known as MI5, would probably have had the monitoring in place during the days before the attack, the committee said.

The committee said MI5 and the other intelligence agencies couldn't have changed the outcome. "We have concluded that, given what the agencies knew at the time, they were not in a position to prevent the murder of Fusilier Rigby," Mr. Rifkind said.

Prime Minister David Cameron said the report raised significant areas of concern but that MI5 would provide a detailed report to the government in the coming months. He added that intelligence agencies have prevented a number of terrorist plots in recent years, including four or five serious ones this year.

Mr. Cameron also said that Internet companies have a responsibility to combat terrorism and that the British government has raised the issue of communications data with U.S. officials at every level, "including with the president."

Tech companies say it is difficult to screen all communications on their systems given the volume and that they need to protect the privacy of their users.

Mr. Rifkind said the one thing that could have prevented the attack was if an online conversation between Mr. Adebowale and an unidentified extremist overseas believed to have links to al-Qaeda had come to the attention of authorities. In the exchange, which took place five months before the attack, Mr. Adebowale expresses his desire to murder a soldier in a graphic manner because of U.K. involvement in Iraq and Afghanistan.

The U.S.-based Internet company on whose system the communication took place hadn't been aware of the exchange prior to the attack. However, it had previously closed some of Mr. Adebowale's accounts because an automated screen indicated they were related to terrorist activity. The committee criticized the company, which it declined to name, for not reviewing those accounts or alerting authorities that it had closed them.

"Had MI5 had access to this exchange at the time, Adebowale would have become a top priority," Mr. Rifkind said. "There is then a significant possibility that MI5 would have been able to prevent the attack."

Mr. Rifkind said companies generally believe they aren't under any obligation to notify authorities of such terror-related material. "However unintentional, they are providing a safe haven for terrorists," Mr. Rifkind said.

Nicholas Winning and Sam Schechner contributed to this article.

Write to Alexis Flynn at alexis.flynn@wsj.com and Nicholas Winning at nick.winning@wsj.com

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