You have different options to consider, since screen readers are just one step in a great accessibility journey.
The attribute is altspecific to imgand tags area. For another element, you can use an attribute titlethat will give access to the tooltip in many browser implementations:
See the HTML5 document :
title , , . ; ; , ; , ; ; . - .
! title , , (, , , , , touch-only, , , ).
title : ( tabindex=0), , javascript , , , , (, ,...).
aria-label
title, aria-label, - . , , aria-label, title.
, , title , aria-label .
<pre aria-label="Welcome!" title="A cute little blob creature">༼ つ ◕_◕ ༽つ</pre>
- .
, , aria-hidden.
<pre aria-hidden="true">༼ つ ◕_◕ ༽つ</pre>