Australia face Bangladesh in a crucial Group A match on Monday at The Oval, just a few miles south of London Bridge, where assailants drove a van into pedestrians at high speed before stabbing revellers.
"The team, support staff and travelling contingent have been accounted for," a Cricket Australia spokesperson said.
"Our security team is working closely with the ICC and (Local Organising Committee) to ensure the safety and security of our players and support staff is paramount.
"At this stage we are comfortable with the level of security being provided to us and will continue to monitor the situation."
The International Cricket Council (ICC) issued a statement later on Sunday, saying safety and security of the Champions Trophy and the women's World Cup, beginning on June 24 in Derby, was "the highest priority".
"Following last night's incident all team hotels went into lockdown and teams, match officials and staff were all quickly accounted for," the global governing body said.
"We will continue to work with authorities over the coming hours and days and review our security in line with the threat levels."
Security was heightened for Sunday's India v Pakistan match at Edgbaston in Birmingham with both teams observing a minute of silence before play.
"The security situation has been very much front and centre of our preparations and we constantly review our procedures to guarantee they are as effective as possible to keep everyone safe," it added.
Sri Lanka Cricket took to Twitter to assure fans that their team, who lost to South Africa at The Oval on Saturday night, was safe.
South Africa, who arrived last month for a three-month tour of England, said their players were "uneasy" following the May 22 night blast at a pop concert in Manchester.
(Reporting by Amlan Chakraborty in New Delhi; editing by Nick Mulvenney)
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