Australia one-day captain Aaron Finch was confident that the duo of Smith and Warner would be able to concentrate on their cricket, playing down the security concerns of both players.
Former captain Smith and fellow batsman Warner returned to international duty earlier this month after completing their bans for their involvement in a ball-tampering scandal in Cape Town last year.
There have long been concerns the players could be on the receiving end of crowd taunts during a long tour of England that later on includes an Ashes series, although England all-rounder Moeen Ali has called for home fans to go easy on the duo.
A report in the Daily Mirror newspaper on Thursday suggested that Warner's manager had sought security assurances from Cricket Australia, with the batsman's wife wanting to give birth to their third child in Britain.
"Since they’ve come back into the squad and the set-up the last couple of weeks they’ve been fantastic," said Finch, looking to lead Australia to a successful defence of the title they won on home soil four years ago.
"They've contributed as much as they can and the morale has been unbelievable.
"Once the World Cup gets under way and you start getting into the tournament, probably the game against England, and then further on the Ashes there's no doubt the crowd will start to play a bit of a part but that's expected.
"No matter where you go the fans play a big part.
"No doubt personally and as an organisation they've got things in place for that, but how they’ve been in the run-up to the tournament has been fantastic."
England and Australia go head-to-head in a World Cup warm-up match in Southampton on Saturday.