A biometric passport (the regular one, in booklet form) - that's what you need. The electronic passport with a chip is a document for online transactions within Russia, but you can't cross borders with it. A lot of people don't know this and end up running into the problem right at the airport. Unfortunately, there's no way around it - foreign border agents simply won't recognize it as a valid travel document.
You'll have to get a new one urgently, yeah. Normally a passport takes about two weeks to make, but if you apply for expedited processing (it costs extra, depends on your region), sometimes it's faster. Check with your regional Interior Ministry or their website to see what options and timeframes are available. If you're flying in the next few days - you probably won't make it, you might have to reschedule your trip.
For future reference, remember this: if you're planning to travel abroad, you absolutely need a biometric passport (red-colored, with a microchip and biometrics, but that's not the same as an electronic passport). An electronic passport is just like any other electronic document - driver's license or vehicle registration - but only for remote services within the country.