99 Avalon xls, dies after started.

99 avalon xls 6 cycliner, auto

Sometimes the engine is kind of shaking after started, and then as soon as I put the shift into reverse it dies.

But as long as the car is running, everything seems fine. It feels normal at high speed, low speed, even at the stop signs.

What can be the cause of this?

Thanks

EDIT: If I give it a little gas, the idle shaking usually gets better. But since I have to lift my foot from gas to brake in order to put the shift into reverse, this does not help.

'Shaking' probably is not the right word for it. When that happens it feels as if the engine is running too slow to maintain its rhythm, like missing beats.

There are/were no lights on.