Tan had sent Mackay an email last Monday in which he heavily criticised the Scot before demanding he resign, or face the sack.
Mackay has made it clear he has no intention of resigning and his departure appeared all but certain despite Dalman, who Mackay considers a close ally, meeting Tan in London on Friday in an effort to earn the Scot a reprieve.
But in a statement on the Cardiff website, Dalman said: "As things stand Malky is in charge for the foreseeable future and will be until something else happens. I don't want to go game by game on this, with people asking if he will be in charge."
He added: "The crisis for the time being is over. The emphasis as of today is for us to create space and dialogue."
But Dalman also made it clear much work is still to be done to repair the damage done to the relationship between Tan and Mackay; the pair had clashed earlier this season over the dismissal of head of recruitment Iain Moody in October.
"I have spoken to Vincent Tan and he has agreed I can go into bat to try to bring a solution to this situation," he said.
"The important thing is that we try to find a way through this predicament. There's good will on Vincent's side. I've not had a chance to talk to Malky just yet, but I will obviously do that as well.
"We need to have further dialogue to see if we can get through this together for the good of the club, which is the most important thing.
"We managed to create space for everyone to work together back in October and we have to see if we can do that again in order to move forward.
"At least we have a platform for dialogue, which gives us an opportunity to try to work our way through this.
"If we wish to work towards a reconciliation, Vincent Tan has offered us that opportunity to move towards that. If it works, it works.
"If it doesn't, it doesn't. But at least I as a responsible person and chairman of this football club have tried my best."
The travelling Cardiff support at Liverpool on Saturday made their feelings towards Tan perfectly clear. There were several 'Tan out' banners in evidence and chants supporting their embattled manager.
Similar scenes had appeared inevitable for the Boxing Day game at home to Southampton.
It remains to be seen if Dalman's statement alters that state of affairs, but the chairman has asked supporters to try and be positive.
"If I had one wish for Boxing Day, it's that they don't hold up 'Tan Out' or 'Malky In' banners, but rather one that says 'Talk to each other,'" he said.