Sporting events and venues in England are conducting major security reviews after 22 people were killed in an attack at Manchester Arena.
The Great City Games, an open and free event for the public, is due to take place in Manchester on Friday.
A spokesman for the organisers said: “We are awaiting advice from the authorities on these events and will provide an update as soon as possible.”
The FA Cup final, EFL play-offs and the PGA Championship are also this week.
An eight-year-old girl was among those killed in Monday’s suicide bombing at Manchester Arena, at the end of a concert by US singer Ariana Grande.
Manchester United cancelled a news conference on Tuesday, due to be held prior to their Europa League final in Stockholm on Wednesday.
The club said: “Our thoughts are with the victims and their families at this terribly difficult time.”
United’s players held a minute’s silence at training on Tuesday, and the club closed its megastore, museum, cafe and stadium tours to the public.
A staff event scheduled for Wednesday has been cancelled by executive vice-chairman Ed Woodward.
Manager Jose Mourinho said: “We are all very sad about the tragic events; we cannot take out of our minds and our hearts the victims and their families.
“We have a job to do and we will fly to Sweden to do that job. It is a pity we cannot fly with the happiness that we always have before a big game.
“I know, even during my short time here, that the people of Manchester will pull together as one.”
Aleksander Ceferin, president of football’s European governing body Uefa, said he was “deeply saddened” and shocked that “so many innocent people lost their lives”.
A Uefa statement said there was “currently no specific intelligence” to suggest Wednesday’s game could be a target for further attacks.
“Uefa has been closely working with local authorities and the Swedish FA for many months and the terrorist risk had been taken into account since the very beginning of the project,” it said.
“Furthermore, a number of additional security measures were implemented following the attacks in Stockholm last April.”
‘Fan safety is of paramount importance’
A number of leading athletes are scheduled to participate at the Great City Games, while a public half marathon and 10km run will be staged in Manchester on Sunday.
Wembley hosts Saturday’s FA Cup final between Arsenal and Chelsea, and the League Two and Championship play-off finals on Sunday and Monday respectively.
A Football Association spokesperson said: “Fan safety is of paramount importance and we have robust security measures in place at Wembley Stadium.
“In collaboration with the Metropolitan Police and the local authorities there will be an enhanced security operation for all upcoming events.
“All supporters are encouraged to arrive for events at Wembley Stadium as early as possible for security checks and to avoid any delays in entering the stadium.”
The English Football League (EFL) added it “takes security issues extremely seriously” and urged supporters travelling to Wembley to “be vigilant of their surroundings at all times, stay alert and not be alarmed”.
Golf’s BMW PGA Championship starts at Wentworth on Thursday.
“As with any major event, security is the highest priority,” said European Tour chief executive Keith Pelley. “It was before Monday night and it remains so.
“We’re in constant dialogue with the police and security services. We are comfortable we will react in the right way if in fact we need to significantly increase our security.”
Cricket’s Champions Trophy will take place from 1-18 June at venues in Birmingham, London and Cardiff.
A statement from the International Cricket Council read: “The ICC and ECB [England and Wales Cricket Board] place safety and security at the ICC Champions Trophy and ICC Women’s World Cup this summer as the highest priority.
“We operate on advice from our tournament security directorate – in conjunction with the ECB and relevant authorities – to ensure that we have a robust safety and security plan for both tournaments.
“We will continue to work with authorities over the coming hours and days and review our security in line with the threat levels.”
England one-day captain Eoin Morgan said his team had met their security advisers on Tuesday morning before Wednesday’s match against South Africa at Headingley.
Morgan says the team have full confidence in the safety measures in place.
“On behalf of the England cricket team, I’d like to offer our thoughts and prayers to everybody in Manchester affected by the tragic events,” said Morgan.
“I’d also like to give our support to those in and around things and those most affected and those who helped out and continue to help out.”
The domestic rugby union season has finished, but the National Counter Terrorism security office has been in touch with Sale Sharks and every other Aviva Premiership club asking for details of any events planned by them over the next couple of weeks.