Can a US citizen leave and enter the US using a foreign passport?

Just a note from recent experience - you can actually get an ESTA for your non-US passport - and I checked with a US border person before doing so (I'd v stupidly left my US passport at home), when going through pre-clearance in Ottawa, Canada, in transit to Brazil - but that doesn't mean you should. I input details of all passports, incl the US one, and the system didn't stop me and nor did the US passport control. But I got taken away just before boarding the U.S.-bound flight on my way home. Had to go get an emergency passport (& the one I left behind has been cancelled) and spend an extra night to do so. Just don't try - you might make it one way but it's unlikely you'll make it both. The airlines get fined, too, so they are quite zealous!

Generally, airlines worry most about you holding a visa for the destination country. I have left the US many times forgetting to return my I-94, but I obviously had an entry record for that passport.

However, it is illegal for US citizens to enter or leave the US on another than a US passport. Since you are a US citizen, you can not obtain a US visa (for your foreign passport) and you are required to enter with your US passport (as clearly stated on the US embassy website): https://uk.usembassy.gov/u-s-citizen-services/u-s-passports/u-s-passport-faqs/u-s-citizenship/

If you plan to re-enter the US with a foreign passport, you might get into trouble! Of course, this is up to the immigration officer, but you will already have issues boarding your flight, as the airline will check for a valid visa/ESTA with the foreign passport you plan to return with.

As a US citizen you can not obtain a visa/ESTA for your foreign passport. During the application process you will be asked if you hold or have ever held US citizenship and will therefore be refused a visa.

You can generally acquire an emergency / temporary travel document or expedite the passport application: http://travel.state.gov/content/passports/english/passports/services/expedited.html

I am a dual Australian American citizen living in Australia, I've gotten an ESTA for my Australian passport. It did ask about being American, I answered yes and it dutifully issued the ESTA.

There will be no problem leaving the US. The airline only wants to check your passport to see if you are have the correct documentation to get off the plane at your destination.

However, it is illegal according to US law for a US citizen to enter the US using a non-US passport. So you'll have problems coming back home unless you make arrangements to have your new passport sent to you while you are away from home.

To the original question I will add that I have travelled between Canada and the USA with my second-last expired US passport, while the last one was with the State Department or in the mail for renewal. No problem, not even secondary inspection.

I have never entered the US with my non-US passport, as I knew it was not allowed. I don't remember about leaving the US. (I don't think the US checks that anyway, some countries do, but not the US). Note: it is not the same thing leaving the US as entering the destination or transit country.

Since this came up it might be worth noting that the actual administrative law being violated is 22 CFR 53.1, and 22 CFR 53.2 has the exceptions which can be trolled for loopholes.

It appears to me that one might be able to legally get away without a valid US passport by flying via Canada with a valid NEXUS card (though I'm not positive; "NEXUS Air kiosks" are an anachronism and, anyway, if they don't like what you are doing they can invalidate the NEXUS card on a whim). Crossing the land border with a WHTI document and flying from and to Canada might be a bit more secure. Having a non-US passport is of no help to an American at all, however.

Could I use my non-US passport to leave the US and return? I have never entered the US with my non-US passport.

You could definitely leave the US without any issues whatsoever, as there's no immigration controls at American airports. Likewise there's no penalty for violating the law which forbids leaving the US without a valid US passport.

Coming back would be a bit more tricky, as US citizens are generally not supposed to be issues ESTAs or visas. And without an ESTA or visa you wouldn't be allowed on the plane back home. However you can escape that issue by flying to Canada or Mexico first and then entering the US overland. US border guards won't be able to deny you entry as long as you convince them you're a US citizen, so at worst you would have to spend a bit more time while they verify your identity. Another option is to receive an emergency US passport at a consulate abroad.

Overall the easiest solution is to simply wait for your passport to arrive and then proceed with your travels.