In the northwestern English city of Manchester, the birthplace of Suffragette leader Emmeline Pankhurst, May hailed the centenary of "a huge and irreversible step towards creating a truly universal democracy".
She noted major advances in the rights of women and other minorities since 1918, but warned of a new tone of "bitterness and aggression" in public debate.
"Women in the 19th century had to contend with open hostility and abuse to win their right to vote," said May, Britain's second female prime minister.
"In the 21st century it cannot be acceptable for any women -- or any person -- to have to face threats and intimidation simply because she or he has dared to express a political opinion."
May called for greater action by social media companies to clamp down on abuse, and announced a review of the law relating to online offensive communications.
During a debate in the House of Commons in London, interior minister Amber Rudd also highlighted how many female MPs face "vile sexist abuse".
"I bear it, like other women in this chamber do, because I know that female voices matter in politics and in life," said Rudd, who is one of six women in May's 23-strong cabinet.
A total of 489 women have been elected to the House of Commons in the past 100 years, while the current parliament is made up of 208 women and 442 men.
The prime minister invited all former and sitting female MPs to a reception on Tuesday evening at Westminster Hall, which was attended by around 520 women.
Calls for pardon
The historic Representation of the People Act 1918 allowed women over the age of 30 and all men to vote, enfranchising around eight million British women.
But the law was not obtained without a struggle, and campaigners have made a fresh call for posthumous pardons for the women who used violence to advance their cause.
The move has been backed by opposition Labour leader Jeremy Corbyn and Scottish Conservative leader Ruth Davidson, as well as descendents of those involved and equality campaigners.
Frustrated with years of peaceful campaigning, Britain's Suffragettes adopted militant tactics in their fight for the vote, chaining themselves to railings, breaking shop windows and blowing up post boxes.
They cut electricity lines, disrupted meetings and even bombed the house of a government minister.
More than 1,000 women were arrested, with many imprisoned. Some went on hunger strike in jail, but were brutally force fed.
Rudd said she understood the campaign, but told the BBC: "It is complicated. If you're going to give a legal pardon for things like arson and violence it's not straightforward."
'Complete their work'
The act which gave women the vote went on display in parliament's central lobby on Tuesday, together with three other crucial laws brought together for the first time.
They included the Parliament (Qualification of Women) Act 1918, which allowed women to become MPs, the Equal Franchise Act 1928, which gave women the vote on the same terms as men, and the Life Peerages Act 1958, which allowed women to sit in the House of Lords as life peers.
A specially-commissioned public exhibition featuring life-sized images of central figures of the suffrage movement was also unveiled in Trafalgar Square.
New Zealand led the way on votes for women in 1893, followed by Australia, Finland and Norway, but Britain's global standing meant its move had global repercussions.
Campaigners argue however that there is still some way to go on women's rights.
"The uncomfortable truth is that gender equality is still an unwon cause," said Nicola Sturgeon, the first minister of Scotland.
She noted the gender pay cap, the continued prevalence of sexual abuse and harassment, and the fact that women still make up only a minority of parliamentarians.
Citing the Suffragette slogan, Sturgeon said: "It falls to us in our generation through 'deeds not words' to complete the work that the suffrage work started."
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