The story was about an American spy on the track of (probably) some Russian spies. For some reason he had a device that enabled him to go backward (forward?) in time by a few minutes. I'm pretty sure that the film was made in America and I think I saw it in either the mid 1960's or (at the latest) the early 1970's. I checked out the following wiki page and at first thought it might have been "Agent for H.A.R.M." (using the logic sci-fi film involving spies) but this proved fruitless.
Could this be Dimension 5?
The spy protagonist has a time travel device:
What happened? What was that device? Did he teleport? No, in fact he time-traveled. Which is later explained as travel to another dimension, "the fifth dimension." Not explained: why they skipped the fourth dimension, or how dimensional travel equals time travel.
It was made in 1966, so it fits your timeframe.
The enemy spies were from Southeast Asia, I think, not Russia.