More than 14 million people will go to the polls next month in an election that is one of the most important since independence

One by one, to the sound of polite applause from a select audience, the seven men and one woman who want to lead Kenya for the next five years walked on to a wide stage in a private school near Nairobi's national park, ready to make history in the country's first televised debate.

Moderators Julie Gichuru and Linus Kaikai, both television journalists, asked the candidates to take their positions behind the podiums and to briefly introduce themselves.

It was a polite, somewhat halting start to a three-and-a-half-hour marathon that gave Kenyans a chance to judge their prospective leaders on their words and policies rather than on who they are – a rarity in a country where politics has traditionally been intertwined with tribal identity, and where politicians often campaign on an "us versus them" platform.

Beyond the walls of the ornate Hogwarts-esque Brookhouse International School, millions of Kenyans were watching on television, listening to their radios, or following the live stream on YouTube.

On Twitter, where Kenyans are the second most active users in Africa, people immediately began tweeting quotes and impressions, making the debate one of the world's top trending topics.

"Tonight has been good – we were united thanks to the debate," tweeted one man, reflecting a sense of pride among many Kenyans commenting online.

If the debate was widely perceived as a positive political milestone, the civil and polite tone seemed worlds away from rising concern that Kenya may be heading for a repeat, or worse, of the politically motivated tribal violence that exploded after the last presidential vote in 2007 and that claimed around 1,200 lives.

More than 14 million Kenyans will go to the polls to elect a president, MPs and county representatives on 4 March in an election that is one of the most complicated and crucial in the 50 years since Kenya achieved independence in 1963.

If no one wins more than 50%, there will be a second round run-off in April. Observers have warned that there is a risk of violence if the vote is tight, or if there is doubt about transparency of process.

Veteran journalist Kaikai showed his combative form with his first question, asking the candidates to talk about the role of tribalism in politics, and pressing the two frontrunners – deputy prime minister Uhuru Kenyatta and prime minister Raila Odinga – on perceptions that their campaigns were exploiting traditional tribal animosities.

The two men are members of Kenya's premier political dynasties, and their rivalry mirrors the relationship between their fathers – Jomo Kenyatta was Kenya's first president and Jaramogi Oginga Odinga was vice president until he fell out with his leader, resigned and founded an opposition party.

Kenyatta is a member of Kenya's dominant Kikuyu tribe, and his running mate, former education minister William Ruto, is a Kalenjin. Odinga is from the Luo tribe, which has never held the presidency.

Both Kenyatta and Odinga rejected the claims that they were running ethnic campaigns. "Tribalism is a cancer that has afflicted this country for a very long time," Kenyatta said. Odinga described tribalism as "a disease of the elite".

Kaikai also asked Kenyatta, who was arguably the most vulnerable going into the debate but who delivered a smooth performance, how he could run the country while facing trial at the international criminal court (ICC) in The Hague for his role in allegedly stoking the violence in 2007. Kenyatta, who has denied any wrongdoing, was quick to reassure the voters that he would be able to govern even while fighting the charges in The Hague. "The job I seek is going to be given by the people of Kenya … who full well know the personal issues I am confronted with," he said.

The moderators asked the candidates to talk about issues such as public finances, education, health and corruption. The candidates rarely engaged directly, and the format meant that interruptions were rare.

Moments of humour were somewhat scarce and restrained, although Odinga raised a few chuckles when he said that it would be difficult for Kenyatta to run the country via Skype from The Hague.

Many observers felt Martha Karua, the only woman standing for president and a former justice minister who is known as "the Iron Lady" because of her tenacity in a male-dominated arena, performed well, especially when she pointed out that nobody got their food from their tribe.

Her tiny red handbag also delighted some online observers.

Amid all the praise for a historic debate, there was also some criticism, with some Kenyans suggesting that having all eight candidates made the format too cumbersome. Polls give Odinga a slight lead over Kenyatta – 46% against 40% in the most recent survey – with the other candidates polling 5% or less.

Some observers might have had difficulty in reconciling the fine words delivered in this public arena with reports of hate speech and intimidation on the campaign trail. More than 400 people have already been killed in 2012 and this year in intercommunal clashes that rights organisations have linked to politics .