Arnold Schwarzenegger and Maria Shriver are keeping their separation civil ... so far.

"I want to take a moment and thank our many friends and family for the tremendous amount of support and love that you have given us in the last 24 hours," the actor-turned-governor said on Tuesday night at the 63rd Israel Independence Day Celebration in L.A., Usmagazine reports.

"I just spoke to Maria an hour ago before I came here. We both were saying the same thing – we're extremely blessed to be surrounded by so many wonderful people, by so many wonderful friends," he added.

"We both love each other very much. We're very fortunate to have four extraordinary children. And we're taking it one day at a time. The bottom line is we want to thank all the people for their great, great support," Schwarzenegger continued.