Witold Waszczykowski said Wednesday the couple came to collect their daughters from the Ariana Grande concert Monday night.
"The London O2 shows this week have been cancelled as well as all shows through June 5 in Switzerland".
"We are sure our fans will understand this decision", the team said, adding that the parade would have diverted police from the bombing investigation.
Grande is scheduled to perform six dates in Australia and New Zealand in September.
Early Wednesday, Manchester police arrested a man at a house just a 10-minute walk from Abedi's home.
Abedi fled Tripoli in 1993 after Moammar Gadhafi's security authorities issued an arrest warrant and eventually sought political asylum in Britain. He was picked up while allegedly receiving a money transfer from Salman Abedi.
Ramadan Abedi, Salman's father, an alleged former member of the Libyan Islamic Fighting Group, was also been seized by masked gunmen yesterday whilst giving phone interviews at his Tripoli home.
Fox reports President Trump condemned the damaging media leaks from the USA on the Manchester bombing ongoing investigations, after UK Police chiefs announced they would stop sharing information concerning the probe with the US. Police sources say he was captured on security camera video at a store in Manchester, possibly buying the backpack used to carry the device.
USA leaks about the British investigation into the Manchester bomber have strained the two countries' "special relationship" and thrown into doubt the sharing of information among the "Five Eyes" intelligence alliance.
Another arrest was made later in Wigan of a man carrying a suspect package.
A woman arrested in the Blackley area of Manchester on Wednesday has been released without charge.
"These searches are connected to Monday's horrific attack on theManchester Arena, but this is a fast moving investigation and we are keeping an open mind at this stage", police said in a statement.
Earlier, Sky News had claimed that they have found evidence linking Salman Abedi to an Islamic State (ISIS) cell operating in Manchester. The report said that British police informed their German counterparts that Abedi had received paramilitary training in Syria beforehand.
The bomber's name, Salman Abedi, was also leaked to the U.S. media despite United Kingdom police not wanting it to be released. "We had the same protests", he told BBC Radio 4.
Britain raised its threat level from terrorism to "critical" late on Tuesday amid concerns that Abedi may have accomplices planning another attack.
Armed police will increase patrols and military personnel will be deployed at events such as concerts and sports matches. He was a British national of Libyan origin, he grew up in Great Britain. Campaigning for the June 8 elections here resumed after being suspended since the arena attack.
A total of 64 people are being treated in hospital, including 20 in critical care, medical officials said.
Police are holding eight people in custody in connection with the attack on a packed concert hall, which killed 22 people.
Interior minister Amber Rudd confirmed on Wednesday that Abedi was known to intelligence services and that it was "likely" he was not working alone.
Wednesday's controversy with the New York Times followed similar episodes in the wake of the attack - including United States sources sharing the terrorist's identity with broadcasters.
"So it is irritating if it gets released from other sources and I have been very clear with our friends that that should not happen again".