Najmul Hossain had never been to a protest before. But for the past fortnight, the 45-year-old Bangladeshi banker has regularly made the short journey to Shahbag Square, a broad, tree-lined thoroughfare in the heart of Dhaka, the capital, to call for the hangings of Islamist politicians accused of war crimes during the country's 1971 war of independence.

On Saturday, Hossain took his six-year-old son with him to the protest, holding a banner with the message, "Razakars [Islamist collaborators] must be hanged". The child carried a toy gun. "My uncle was killed in 1971 by the Pakistan army," Hossain said. "I cannot forgive those who killed and stood with the killers."

On the other side of town, Shamsuz Zaman, a 58-year-old timber trader, is equally fired up but for different reasons when discussing Shahbag. "War crimes are just an excuse," he said. "Bangladesh has so many problems. The people who are leading these mobs are atheists who insult Islam, God and the prophet." The gulf between those who think the Shahbag protests – the largest in two decades, that some are calling the Bangladesh spring – is a movement for righting a historical wrong and those who consider it to be a veiled, government-sponsored attempt to curb the influence of Islam has never been wider.

At least five people have been killed since Friday in countrywide violence, including two opposition activists who were shot dead by police on Saturday morning, local police officials confirmed. The violence began when conservative Islamists clashed with police after Friday prayers, protesting against what they said were blasphemous online posts by bloggers at the forefront of the Shahbag protests.

An alliance of Islamist parties called for a general strike on Sunday to protest at what they see as the use of excessive force against opposition activists. The police said they were trying to maintain law and order.

Much of the mistrust is rooted in Bangladesh's tumultuous past. Bangladesh declared independence from Pakistan in 1971. The Pakistani army fought and lost a brutal nine-month war with Bengali fighters and Indian forces that had intervened. Hundreds of thousands of civilians died, many of them at the hands of Islamist militia groups who wanted the country to remain part of Pakistan.

In 2010, Sheikh Hasina, the prime minister, and daughter of wartime political leader Sheikh Mujibur Rahman, set up a war crimes tribunal to investigate atrocities committed during the 1971 conflict – a move she said would bring closure for victims and families and heal the rifts of war.

The leader of the opposition Bangladesh Nationalist Party (BNP), Khaleda Zia, the widow of the independence war's best-known military commander, has accused Hasina of politicising the tribunal and conveniently using it to hound her political enemies. All of the 10 people indicted for war crimes by the tribunal are opposition politicians, eight of them from the Jamaat-e-Islami, the country's largest Islamist party and an ally of Zia's BNP.

Despite criticism from human rights groups about politicisation and procedural flaws, the war crimes tribunal has remained broadly popular. Last month the tribunal sentenced a former member of the Jamaat-e-Islami to death for his role in the 1971 war. On 5 February, a verdict of life imprisonment was delivered against Abdul Quader Molla, a senior leader of the Jamaat-e-Islami, sparking the Shahbag protests. Since then, hundreds of thousands of people have converged on Shahbag, the hub of protests, adamant that all of the men on trial for war crimes must receive the death penalty.

This week President Zillur Rahman signed into law an amendment to the statute that governs two functioning war crimes tribunals, giving prosecutors the power to seek stiffer sentences on appeal, a key demand of the protesters. The new law also gives the government the power to charge entire organisations with war crimes, another Shahbag demand.

The protesters, however, have ratcheted up the pressure, saying they will remain camped out in Shahbag until all of the accused currently before the war crimes tribunal are given the death sentence. They have pushed a broader set of demands, including banning the Jamaat-e-Islami and confiscating businesses linked to Islamist groups.

"We are protesting 40 years of injustice," said Lucky Akter, 23, a student and member of a leftwing political party who has become one of the faces of the protest with her fiery slogans. "We want those who collaborated with the Pakistan army hanged and their finances cut off."

Analysts say the broader demands from the Shahbag gathering show how the rifts of the past continue to play a major role in Bangladesh's present. "There is an ideological basis to protests," said Muhammad Musa, a political commentator and former newspaper editor. "There is the widespread perception that the Jamaat-e-Islami supported Pakistan during the war and should answer for this."

On Saturday a crowd in the thousands gathered in Shahbag, joining a hardcore group of activists, waving flags and chanting slogans such as, "Hang, hang, hang them all!" and, "The weapons of '71 must fire again!"

The Jamaat-e-Islami, whose activists have waged violent street agitations against the tribunal, says it is being scapegoated. Shafiqul Islam Masud, a party leader, said many people were blurring the difference between a political position and war crimes. "There are only about 50 people active in the party now who took any kind of a political position 42 years ago," he said. "It's possible some of them did not want to secede from Pakistan, but that's a far cry from war crimes. The party accepted the sovereignty of Bangladesh and is a registered political party, represented in parliament."

Sam Zarifi, the Asia director for the International Commission of Jurists (ICJ), a Geneva-based legal advocacy, said a fair trial process was necessary to heal the wounds of the war. "It is very important that victims of 1971 get justice," he said. "But justice must be ensured through a fair and transparent trial process. Unfortunately, if judges are intimidated by mass protests into handing out death sentences, that's not justice and may unleash yet another cycle of violence."

Such words of caution are dismissed by Shahbag protesters as intellectual posturing. The crimes of 1971, which have been thrust into the spotlight by the tribunals, have dominated Bangladeshi newspapers, airwaves and websites, uniting the youth of Dhaka in an unprecedented manner.

"The people have spoken," said Akter. "Now it is up to the courts and the politicians to implement."

Analysts say the protests have worked to the government's advantage and distracted attention from economic and governance issues the opposition had been agitating about. Last year, Hasina scrapped a constitutional provision under which a non-partisan caretaker government oversees elections, leading to the opposition threatening a boycott of parliamentary elections due in early 2014.

"Had it not been for the protests, now we would all be focusing on next year's elections and looking at the government's record in office and the opposition's pledges," said Zafar Sobhan, editor of the Dhaka Tribune, an English daily. "Now, all bets are off and elections seem a distant concern. It is hard to see how things will revert to politics as usual after this."

Asif Mohiuddin, a co-ordinator of the bloggers' network that called for the Shahbag protests, is keen to point out the group's struggle did not start with Shahbag. "We have been waging war on religious fundamentalists on the blogs for years," he said. "Shahbag has been successful because people are so outraged by the war crimes."

Yet some analysts say the narrative of a secular revolution leading the country towards a democratic future may be simplistic. The protests have polarised the country and led to tensions between those who identify themselves as progressive.

"Many are worried about the Shahbag protest's aggressive tone and narrow focus on the death penalty," said one of the editors of alalodulal.org, an English language blog. "I wish the unique energy of Shahbag could be channelled into the energy and desire to do thorough research, digging out solid evidence that can result in fair trials that do not require government contortions."

• The headline on this article was changed on 24 February.