Advocaat paid a surprise visit to the Russian squad on the last day of their training camp and waited for Hiddink to arrive.
The two coaches shook hands and embraced each other in front of several dozen television and photo journalists.
Advocaat had criticised Hiddink for naming six Zenit players for the February 8-11 camp in Turkey, saying it would interfere with preparations for this month's UEFA Cup last-32 tie with VfB Stuttgart.
Hiddink has agreed to become Chelsea's caretaker manager until the end of the season in addition to his job with Russia.
"He (Advocaat) was also a national team coach so he should know it's always a give-and-take situation," he said. "You can never have it your own way, you must always find a compromise."
"It would take players 15-20 minutes at most to drive from one place to another."
"We don't have to be friends but it's not true we don't talk. Last week I sent him a text explaining everything. I didn't talk to him because he doesn't like to talk much on the phone."
"It's not a problem anymore, we can talk," he told Reuters, dismissing media reports that the two Dutchmen would not speak to each other.
"We still have our differences because he (Hiddink) cares about the national team and I must care about my club," he said.
"It's not a big problem for me if he takes six of my players away for three days but, of course, I would have preferred to keep them at the club."
"No, I would say 'have a good flight (to London)'," Advocaat said.
