"ULN2003 has surge supressor diodes on chip"

I presume you mean protection diodes to stop the back-emf caused by de-energising the relay coil from zapping the chip?
Note that they don't actually stop the surge - just direct it along a path which can safely hadle it. The surge still happens.

There will also be a surge of current into the coil when you energise it.

There may also be arcing and other nasty transient effects at the contacts when they open/close, and also in the connected loads.

What load(s) are you driving?

"The worst thing is that external interrupts get actuated."

Sounds like inadequate noise protection.