Late on Friday, official sources in New York appeared to accept that the two men shot and wounded during the previous day's dawn raid on a Brooklyn flat were associated with the Middle Eastern terrorist group, Hamas - the same group that had admitted responsibility for the Jerusalem suicide attack the previous day. By yesterday, however, that link was disputed - apparently by Hamas itself.
A leaflet faxed to international news agencies on Saturday said: "We deny any connection between us and the prisoners or the accusations against them. Hamas does not consider the American people an enemy and it does not target any of its communities."
Earlier this year, in a move supposedly designed to prevent the man in question from becoming a martyr to the Palestinian cause, the United States allowed a senior Hamas political figure, Moussa Abu Marzook, to go to Jordan and ignored an Israeli request for his extradition. Mr Marzook added his voice to the denial yesterday, saying that it was "ridiculous and a total lie" to say Hamas had anything to do with the two men under arrest in Brooklyn.
The only evidence cited by US officials to connect the two men, Gazi Ibrahim Abu Mezer, 23, and Lafi Khalil, 22, with Hamas was a small amount of Islamic literature found in the flat, a vague expression of sympathy with the Jerusalem bombers made by Mr Mezer at the time of his arrest, and what was said to be the draft of a suicide note.
Families of the two men - both Palestinians from the West Bank - who were contacted by reporters also expressed strong reservations about the likelihood of their involvement in terrorism. Mr Mezer and Mr Khalil, who are in hospital recovering from gunshot wounds, have been charged with conspiracy to blow up the New York subway and possession of explosives.
Meanwhile, the spotlight shifted away from the alleged bomb plot to how the men arrived in the US. There was consternation over reports that Mr Mezer had been caught three times trying to enter the US illegally from Canada.
The third time, it is said, he declared that he was considered a terrorist in Israel and asked for political asylum. After his first request was turned down, he decided against reapplying and was given 60 days to leave. That period expires on 23 August.
At least one of the men arrested in possession of bomb-making equipment, therefore, was in the US with the knowledge of the immigration authorities. The question that begs to be answered is whether this was a result of lax immigration procedures, as the mayor of New York, Rudolph Giuliani, charged, or whether the intelligence services had deliberately allowed him in for the purpose of tracking or infiltrating terrorist groups.
Israeli security agents flew to New York at the weekend to assist the FBI in its investigation. At the same time it was reported that the US Middle East trouble-shooter, Dennis Ross, was returning to the region later this week with a revised formula for kick-starting Israeli-Palestinian peace talks. The key elements will remain an Israeli settlement freeze, balanced by a Palestinian drive against violent Islamic resistance to the Oslo accords.
But in the wake of the twin suicide explosion in a Jerusalem market, which killed 13 Israeli civilians last week, Mr Ross is expected to strengthen demands that Yasser Arafat curb the men of the bomb and the gun.
Israeli security sources admitted yesterday that they still had no firm lead on the identity of the two bombers in the Mahane Yehuda market.