Theodore Scardino, one of the firefighters "significantly wounded" in the shooting in Webster, New York, has spoken since treatment, say Strong Memorial Hospital staff.
Scardino is able to breathe on his own, but staff said both he and Joseph Hofsetter were "at risk" and being monitored for bleeding.
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Thousands of soldiers who died in the Battle of the Somme will be remembered today at commemoration events across the UK and France.
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Theresa May's bid to become Tory leader has won the backing of senior cabinet ministers including Michael Fallon and Patrick McLoughlin.