At least four Germans were thought to be on the hijacked planes
Speaking before an emergency cabinet session on Thursday, Mr Straw said the final toll was likely to exceed the "middle hundreds".
Ruth McCourt from the Republic of Ireland and her four-year-old daughter, Juliana, were on board the United Airlines flight which ploughed into the side of the World Trade Centre's south tower.
But her brother, John, who watched the crash on television feared first of all for their brother Ronnie.
He had just entered the WTC building as the plane crashed and made a miraculous escape.
"[Ronnie] went through the front door on the ground floor and the lady who was about three seconds in front of him was hit by a terrific fireball and she was horrifically injured," John Clifford said.
'Absolutely horrific'
It was only later that John became concerned about Ruth, who lived in Connecticut. She was due to leave Boston's Logan airport to fly to Los Angeles.
"To watch two planes crash into the two buildings and then discovering afterwards that your sister and your niece were on the plane was absolutely horrific," he said.
The close ties between Ireland and the US and the massive Irish-American diaspora have left the country, described by some as the "51st state," feeling particularly stunned by Wednesday's events.
In Germany, officials said they believed a German woman had been on board one of the planes.
"We have relatively certain information about an air stewardess, a German, who was in an aircraft which was used as a weapon of terror," Ludger Volmer from the German Foreign Office said.
Day of mourning
The Prime Minister of the state of Baden-Wuerttemberg said three people from that region were believed dead.
It is almost certain that they were the managing director, the head of personnel and another senior member of the BTC firm. They are also believed to have been on board one of the planes.
Mr Volmer warned that the number of German victims was likely to rise.
"We know that several German firms were located in the World Trade Centre and the affected buildings round about and that employees may have been there at the time of the catastrophe," he said.
In France, the Credit Agricole banks said that 86 of its expatriate employees who worked on the 92nd floor of the World Trade Centre were unaccounted for.
A day of mourning and a three minute silence for all the victims of the attacks will take place across the European Union's 15 member states on Friday.