The Prime Minister confirmed that there were suspicions that British servicemen had been killed with explosives obtained from Iran, possibly through the Iranian-backed Hizbollah in Lebanon.
British officials have suggested that the Iranian government may be seeking to pressure Britain into relaxing its opposition to Tehran's nuclear programme, although both Iranian and Iraqi leaders yesterday poured cold water on the claims.
Mr Blair used a high-profile meeting yesterday with the Iraqi President, Jalal Talabani, to issue a stern warning to Iran.
Speaking at a joint press conference with President Talabani in Downing Street, Mr Blair said: "I want to make it very, very clear - and this has been made clear to the Iranian government and I make it clear again - the British forces are in Iraq under a United Nations mandate, they are there with the support of the Iraqi government.
"There is no justification for Iran or any other country interfering in Iraq. Neither will we be subject to any intimidation in raising the necessary and right issues to do with the nuclear weapons obligations of Iran under the Atomic Energy Agency treaty."
The Prime Minister conceded that there was no proof yet of Iranian involvement. He also admitted he had been caught out by the way the allegations, which have been discussed in private by British officials, had surfaced at a time when President Talabani was on a visit to London, and hardliners in Washington were pushing for punitive action to prevent Iran from developing a nuclear programme.
But he insisted: "What is clear is that there has been new explosive devices used, not just against British troops, but elsewhere in Iraq.
"The particular nature of these devices lead us either to Iranian elements or to Hizbollah, because they are similar to the devices used by Hizbollah, which is funded and supported by Iran."
Tehran has strongly denied the British claims, and yesterday received the support of Iraqi government leaders who publicly played down British claims linking Iran to the killings of British soldiers in Iraq.
Just hours after Mr Blair issued his warning to Tehran not to interfere in Iraq, President Talabani said during his visit to Britain that there was "no evidence" linking the Iranian government to the attacks.
The Iraqi President added: "I asked some Iranian brothers about this and they told me that they had no wish to make trouble for Iraq.
"Finding this device did not mean it came from the government of Iran. Where is the evidence? Maybe they gave it to some other group and they gave it to someone else."
In Baghdad, Iraq's Prime Minister, Ibrahim Jaafari, also denied the charges, saying: "Such accusations are baseless and we do not agree with them at all. Relations between Iran and Iraq are very friendly, and we are proud of the situation."
The Iranian ambassador to Britain, Seyed Mohammed Hossein Adeli, challenged Mr Blair to produce proof to back allegations that his country had supplied explosives used by Shia groups used to kill eight British soldiers.