Zenit Automat: New but with a Strange light meter

I bought a 1991 Zenit Automat a month ago. It looked new and in excellent condition, but the light meter behaves strangely: when checking with an external light meter or in a bright environment, the aperture-shutter ratio is correct, but in low light it overexposes by a stop. Sure, I can use the correction dial, but it's not convenient because I have to judge the lighting conditions myself. I've seen how to disassemble it in some YouTube videos: perhaps there's a potentiometer I can adjust for low light?

The Internet says that camera should have four PX625 batteries (mercury) -- which are no longer available.

What batteries are you using in it?

First of all, thank you for your reply and for the helpful comments you made. Along with the camera, I found two new 4LR44 batteries (6v) from the previous owner, and I thought they were fine. You're right; I see online that this camera used 4 PX 625 1.35V batteries, for a total of 5.4V. The 1989 manual lists Soviet RC-53 1.25V batteries, for a total of 5V. A difference of just 1V could cause the light meter to malfunction! I'm looking for solutions: aside from the MR-9 adapter, which is too expensive (you need four), do you know of any alternatives?

1.25 volt is likely a typo: The voltage is determined by the battery's chemistry.

Are your meter readings being influenced by light entering the camera's eyepiece? I've noticed that KMZ-made Zenit cameras can be particularly susceptible to this, including cameras made as late as 2005.