Government ministers have asked the US to order American websites hosting al-Qaeda videos to remove them.
Security minister Baroness Neville-Jones is reported to have recently told Washington officials the sites incited murder and would be banned in the UK.
It comes after a court heard a student found guilty of stabbing an MP in east London was inspired by a cleric linked to the air cargo bomb plot.
Roshonara Choudhry, 21, was convicted of attempting to murder Stephen Timms.
Her trial at the Old Bailey heard that she attacked the Labour MP for East Ham because she was angry at him for voting for the Iraq war.
Mr Timms was stabbed twice in the stomach at a constituency surgery in Newham, east London, in May.
Ahead of the attack, Choudhry was said to have watched online sermons by Anwar al-Awlaki, a radical American Muslim cleric of Yemeni descent.
More than 5,000 videos featuring Mr al-Awlaki are available on YouTube. Investigators have also linked him to the US army base killings in Fort Hood, Texas, last year's Christmas airline bomb attempt, and the failed Times Square bombing in New York.
The head of MI5, Jonathan Evans, has also expressed concern about the influence of Mr al-Awlaki, who has been connected to al-Qaeda in the Arabian Peninsula by the US.
Last week, Lady Neville-Jones addressed the influential Brookings Institute in Washington on the government's security strategy.
According to the Daily Telegraph, in private remarks to the institute she later addressed the issue of websites hosting extremist material, saying: "When you have incitement to murder, when you have people actively calling for the killing of their fellow citizens and when you have the means to stop that person doing so, then I believe we should act.
"Those websites would categorically not be allowed in the UK. They incite cold-blooded murder and as such are surely contrary to the public good.
"If they were hosted in the UK then we would take them down but this is a global problem. Many of these websites are hosted in America and we look forward to working even more closely with you to take down this hateful material."
A Home Office spokesman said the government always pressed for jihadi material to be removed from the internet.
"Where sites are hosted abroad our ability to close them down is limited. Nevertheless, we work with our overseas counterparts to encourage them to remove them," the spokesman said.
Choudhry, who was also convicted of two counts of possessing an offensive weapon, will be sentenced later at the Old Bailey.
She failed to appear in the dock during the two-day trial after telling her barrister she did not recognise the jurisdiction of the court.