Turkey accepts that atrocities were committed but argues there was no systematic attempt to destroy the Christian Armenian people. It says many innocent Muslim Turks also died in the turmoil of war.
A memorial service was held in Turkey on Friday and its prime minister, Ahmet Davutoglu, said the country would "share the pain" of Armenians. But he reiterated Turkey's stance that the killings were not genocide.
Turkey also hosted ceremonies on Friday to mark the 100th anniversary of the start of the Battle of Gallipoli.
However, the actual fighting there began on 25 April, and Armenian President Serzh Sargsyan has accused Turkey of "trying to divert world attention" from the Yerevan commemorations.
After a flower-laying ceremony in Yerevan, Mr Sargsyan addressed the guests, saying: "I am grateful to all those who are here to once again confirm your commitment to human values, to say that nothing is forgotten, that after 100 years we remember."
In his address, French President Francois Hollande said: "We will never forget the tragedies that your people have endured."
France has been a strong advocate of recognising the killings as genocide and President Hollande has pushed for a law to punish genocide denial.
Russian President Vladimir Putin described the killings as "one of the most tragic disasters in the history of humankind" which "shook the whole world".
"There cannot be any justification for mass murder of people," he said. "Today we mourn together with the Armenian people."
Commemorations in Yerevan drew to a close with a candlelit procession. People carried flowers to the city's memorial late into the evening.
In Lebanon - home to one of the largest Armenian diasporas - tens of thousands of people attended a march and commemoration service in Beirut
In Jerusalem, Armenian priests held a two-hour mass in the Old City. Posters outside the church called on Turkey to recognise the mass killings as genocide
And in Tehran, hundreds of Armenian-Iranians attended a rally from an Armenian church to the Turkish Embassy.
At the scene: BBC's Rayhan Demytrie in Yerevan
The purple forget-me-not is the symbol of the centenary. It can be seen everywhere in Yerevan: from window shops and windscreen stickers, to lapel pins that many are proudly wearing.
There is also a centenary slogan which reads "I remember and demand".
But what is it that the Armenians are demanding? I asked some of the people in Yerevan's Mashtotz Avenue.
"We demand fairness from the world community, that's it," said Sergey Martirossyan, "but for me personally it won't make any difference. What we actually need in Armenia is for the government to take serious steps towards economic growth."
During his 2008 presidential election campaign, then senator Obama had vowed to "recognise the Armenian genocide" and in his new statement said: "I have consistently stated my own view of what occurred in 1915, and my view has not changed."
However, his phrasing has angered Armenian Americans.
Bryan Ardouny, executive director of the Armenian Assembly of America, said in a statement: "President Obama's exercise in linguistic gymnastics on the Armenian genocide is unbecoming of the standard he himself set and that of a world leader today."
German MPs are meanwhile debating a non-binding motion on the genocide issue, a day after President Joachim Gauck used the word to describe the killings.
Turkey reacted angrily to Mr Putin's address.
"Considering the mass killings, exiles... that Russia has carried out in the Caucasus, Central Asia and in eastern Europe over the past century... we think it should be the one that knows best what a genocide is and what its legal dimensions are," a foreign ministry statement said.
Earlier this month, Turkey recalled its envoy to the Vatican after Pope Francis also used the word genocide.
In Turkey on Friday, the media largely focused on Gallipoli, but one newspaper, Cumhuriyet, carried a surprise headline in Armenian - "Never Again".
"The wounds caused by the events which took place during the Ottoman Empire are still fresh. It is time to face up to this pain which paralyses the human mind, the feeling of justice and the conscience," it said.
What happened in 1915?
Hundreds of thousands of Armenians died in 1915 at the hands of the Ottoman Turks, whose empire was disintegrating.
Many of the victims were civilians deported to barren desert regions where they died of starvation and thirst. Thousands also died in massacres.
Armenia says up to 1.5 million people were killed. Turkey says the number of deaths was much smaller.
Most non-Turkish scholars of the events regard them as genocide - as do more than 20 states, including France, Germany, Canada and Russia, and various international bodies including the European Parliament.
Turkey rejects the term genocide, maintaining that many of the dead were killed in clashes during World War One, and that many ethnic Turks also suffered in the conflict.