British newspapers The Guardian and The Sun reported that British officials are to present evidence on Wednesday backing up their claims that the sailors were in Iraqi territorial waters.
The evidence is to include maps, co-ordinates and photographs, according to The Guardian.
The move may be part of what Blair said on Tuesday would be a "different phase" of the dispute.
Britain insists that the eight sailors and seven marines held by Iran were conducting "routine" anti-smuggling operations when they were seized at gunpoint in the Shatt al-Arab waterway in the north of the Gulf on Friday.
Iran says they had illegally intruded into Iranian waters.
Britain's efforts to have the sailors and marines freed have so far been unsuccessful.
A Foreign Office spokesman said Beckett had spoken "in very robust terms" with Manouchehr Mottaki, her Iranian counterpart, but Beckett cut short her visit to Turkey on Tuesday to return to parliament after talks with Mottaki were felt to have run their course.
In Tehran, Mohammad Ali Hosseini, an Iranian foreign ministry spokesman, denounced Britain's stand on the issue.
"The media campaigns and provocative ... remarks regarding the violation of Iranian territorial waters by the British sailors are doing nothing to help settle the affair," he said.
"The British service personnel entered Iranian waters illegally and the case will follow its legal and judicial course."
Hosseini said that British diplomats would be able to meet the 14 men and one woman, once investigators had finished questioning them about what they had been doing in Iranian waters.
The EU has demanded the sailors' release and the US has expressed its "concern and outrage" over the situation.
The German foreign ministry said on Tuesday that it had called in the Iranian ambassador to Berlin and reiterated a demand for the immediate release of the British naval personnel.