PM hails McGuinness's 'essential contribution to journey from conflict to peace'
The Prime Minister said the former IRA commander "played a defining role" in leading the Republican movement away from violence.
But Mrs May made clear she did not always "see eye to eye" with the former deputy first minister and could "never condone" his terrorist past.
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Hide AdIn a statement, she said: "First and foremost, my thoughts are with the family of Martin McGuinness at this sad time.
"While I can never condone the path he took in the earlier part of his life, Martin McGuinness ultimately played a defining role in leading the Republican movement away from violence.
"In doing so, he made an essential and historic contribution to the extraordinary journey of Northern Ireland from conflict to peace.
"While we certainly didn't always see eye to eye, even in later years, as deputy first minister for nearly a decade he was one of the pioneers of implementing cross-community powersharing in Northern Ireland. He understood both its fragility and its precious significance and played a vital part in helping to find a way through many difficult moments.
"At the heart of it all was his profound optimism for the future of Northern Ireland - and I believe we should all hold fast to that optimism today."