Warner offered unconditional apologies for his altercation with England player Joe Root in a bar after Australia's opening game loss to the hosts in the ongoing Champions Trophy.
"I'm here today to apologise publicly and put my hand up and say I am responsible for my actions. I am extremely remorseful. I have let my team-mates down, the support staff, myself and my family," Warner told reporters in a jam-packed press conference here.
Clarke, who accompanied Warner to the press conference, urged him to watch his conduct.
"Although the punishment for David is quite harsh, that's the reality when you play for the Australian cricket team," Clarke said.
"This is not an IPL team, this is not state cricket, it's not county cricket, when you play for Australia there are standards you have to uphold," he added in a stern warning.
"I definitely remember the night. It started out with a few drinks in the bar and as a team we went to the Walkabout. I made a mistake and I put my hand up," he said.
"I have exchanged text messages with Joe. He accepted my apology, which I am thoroughly grateful for."
Warner, fined some weeks back for his twitter rant against a couple of Australian journalists who criticised the IPL, rejected suggestions that he was facing a drinking problem.
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