The controversial Hindu nationalist leader Narendra Modi has pledged to work for all 1.25bn of his fellow Indians in his first speech after winning a historic landslide victory to take power in the world's largest democracy.

"Brothers, sisters, you have faith in me and I have faith in you," Modi, 63, told an ecstatic crowd in the town of Vadodara, from where he stood for election in the five-week poll. "The people of this country have given their verdict. This verdict says we have to make the dreams of 1.25bn people come true. I must work hard."

With most of the 550m votes counted, Modi's Bharatiya Janata party (BJP) appeared to have far exceeded all predictions and, with existing allies, were set to win as many as 350 of the 543 elected seats of India's lower house.

The Congress party, which has been in power since 2004 and for all but 18 of the last 67 years, appeared to be heading for its lowest ever tally, set for a mere 60 seats by mid afternoon.

Experts say the political landscape of India has been transformed. The vote is the most decisive mandate for any Indian leader since the 1984 assassination of prime minister Indira Gandhi propelled her son Rajiv to office.

World leaders rushed to telephone the new premier. Nawaz Sharif, the prime minister of neighbouring Pakistan, with which India has fought four wars, invited the new leader to visit.

The US president, Barack Obama, did likewise, even though Modi was barred from the country less than 10 years ago under a law preventing entry to foreigners who had committed "particularly severe violations of religious freedom", Associated Press reported.

Modi, who has been dogged by accusations of sectarian prejudice, appeared to make an effort to reassure those within India and beyond its borders who fear he will prove a divisive leader. "To run the country we need to take everyone with us, all together and I seek your blessings to succeed in this endeavour," he said.

The former tea seller who started his political career with a far right Hindu revivalist organisation promised "good times ahead". In a second speech hours later, Modi invoked Mahatma Gandhi and stressed that "the only solution to every problem is [economic] development – without which India's destiny will not change".

Though a BJP win was expected, few predicted such a crushing victory. For 25 years India has been governed by coalitions, but the size of Modi's mandate means he will not have to work with allies and can set his own agenda. The party's regional strength is likely to be reinforced at local elections in coming months.

Narendra Modi prepares to speak to supporters after his victory in India's elections. Photograph: Kevin Frayer/Getty Images

Such power held by such a polarising figure will prompt some concern internationally. Ravi Shankar Prasad, a senior leader of the BJP who has been tipped as a potential foreign minister, told the Guardian that India would be "power with dignity, with responsibility and of constitutional integrity."

Prasad said however that though the BJP "wishes well for Pakistan", the neighbouring state needed to understand that "terrorism promoted from its soil would not be tolerated".

Supporters, who thronged the BJP headquarters in Delhi on Friday to sing, explode firecrackers, bang drums and chant support for Modi said he would bring honest government, efficient administration and much-needed economic reforms in the troubled nation. "I am elated. It's time for change," said Gautam Sood, 28, a student.

A member of an Indian band performs outside the BJP headquarters in Delhi. Photograph: Money Sharma/EPA

The elections saw around 100 million first-time voters cast a ballot. Support amongst the young appears to be one key reason for the BJPs success. Another is inroads made into rural areas and traditional "votebanks" of the Congress party, such as those at the bottom of the caste system, India's tenacious social hierarchy.

Modi's "Development For All" message appeared to have struck a chord with frustrated voters, particularly the young, across the nation. It also countered accusations of sectarian prejudice, allowing BJP campaigners to argue that they believed in genuine equality because the party wants no communities to receive special treatment.

At the Congress headquarters, only a mile from those of the BJP, there was a very different mood. "It is very disappointing for us all, but we accept the verdict of the people. Congress has bounced back before and we are confident that we will bounce back again," said Rajeev Shukla, a former minister and senior party official.

The outgoing government was hit by allegations of corruption, its failure to rein in runaway inflation and faltering growth. India needs to create 10m jobs each year for new jobseekers alone, an area where the Congress officials admit they had "difficulty".Others blamed the defeat on a failure to communicate the party's achievements in their 10 years in power.

Rahul Gandhi. Photograph: Raveendran/AFP/Getty

Rahul Gandhi, 43-year-old scion of south Asia's most famous political dynasty and vice-president of Congress, retained his own seat of Amethi, but by a hugely reduced margin. The Cambridge-educated former management consultant has struggled to connect with voters and failed to develop any significant momentum throughout the campaign. Congress officials nonetheless rallied around the Gandhi family. "This is not about one particular leader or individual," said Salman Soz, a party official.

But at a chaotic press conference late on Friday afternoon, Gandhi admitted Congress had done "pretty badly" and accepted responsibility for the party's worst ever defeat.

Sonia Gandhi, the president of Congress, called on the new government to avoid divisive policies and said her own party would focus on grassroots work. The 67-year-old won again from the constituency of Rae Bareli, an exception in a rout of dozens of senior Congress figures.

Ravi Shankar Prasad, the BJP leader, said the elections had revealed a "tectonic shift. The politics of dynasty, entitlement and inheritance has been rejected in favour of the politics of initiative and accomplishment based on hard work," he said.

Since being named as his party's candidate last September, Modi has flown more than 185,000 miles and addressed 457 rallies in a slick, presidential-style campaign that has broken the mould of Indian politics. A huge social media effort has reached out to voters across the nation. Modi received more than seven times the media coverage of his chief rival, one study showed.

Modi has promised that a BJP government would take decisive action to unblock stalled investments in power, road and rail projects to revive faltering growth. Indian stockmarkets soared early in the day as results began to be clear.

However, relations between India's 150 million Muslims and the Hindu majority, as much as development, was a key theme as candidates traded accusations of seeking to win votes through targeting particular communities or raising sectarian tensions.

BJP supporters wearing masks bearing the image of party leader Narendra Modi as they celebrate the election in Siliguri. Photograph: Diptendu Dutta/AFP/Getty Images

Modi has been accused of allowing, or even encouraging, riots in 2002 in the state of Gujarat, which he has run for 13 years, in which around 1,000 people, largely Muslims, died. The violence followed an arson attack on a train carrying Hindu pilgrims which killed 59. A supreme court investigation found insufficient evidence to support the charges against Modi, who has always denied any wrongdoing.

Party officials defended his record on Friday. "Let our work speak for us. Gujarat has the highest economic growth rate for Muslims in the country," said Prasad. "The myths have been broken. Mr Modi will govern for all India and all Indians."

In the key battleground state of Uttar Pradesh, which is particularly prone to sectarian violence, the BJP appeared set to win 70 or more of 80 seats, with around 40% of the vote share. The newly formed Aam Admi (common man) party, which has promised to revolutionise Indian politics and purge corruption from public life did not make the breakthrough some had hoped for, winning only four seats.

Ashutosh, who uses only one name, a former journalist who stood for the AAP in Delhi but lost, said the result was a "disappointment" but that an increase in the party's vote share in the capital from 29% to 33% was "a silver lining". He added: "We need to work on our organisation, we need to build a solid base, we need an effective communication system and to fine tune our ideological moorings."

The AAP's leader, Arvind Kejriwal, lost in a three-way fight with Narendra Modi, who stood from two constituencies, as permitted under India's electoral laws, and a Congress candidate. Kejriwal, a former tax inspector turned anti-graft activist, came second.

Arvind Kejriwal, the leader of India's Aam Admi party, pictured releasing his election manifesto in Delhi in April. Photograph: Chandan Khanna/AFP/Getty Images

Influential female regional leaders had mixed results. In Tamil Nadu, chief minister Jayalalithaa Jayaram's party, the All India Anna Dravida Munnetra Kazhagam, was reported to be leading in 37 out of 39 seats, and Mamata Banerjee, chief minister of West Bengal, had done well but Mayawati Kumar, a key power broker in Uttar Pradesh had been wiped out.

One key question in coming months will be the influence on the new government of the vast conservative Hindu revivalist organisation where Modi started his career as an activist. The Rashtriya Swayamsevak Sangh (National Volunteer Union) has been heavily involved in the campaign and Modi and many other senior officials of the BJP, which is independent of the RSS though ideologically close, are still members of the organisation.

"The BJP is a cadre-based party and we are the cadre. Ideology and cadre is what makes BJP win," Rajeev Tuli, an RSS spokesman told the Guardian at the Delhi headquarters of the organisation, which has been banned by Indian authorities three times.

Analysts say the RSS and other hardline groups will now push hard for the fulfilment of core long-term demands such as the construction of a Hindu temple on the site of a demolished mosque in the northern town of Ayodhya.

Aides described how Modi had watched the results come in alone in the chief minister's residence in Gandhinagar in Gujarat. "He took no calls, just made a few around the country to key people. That's his way of doing things, very calm, very focused," one said.

Modi's visit to his 95-year-old mother had however been arranged in advance. He touched her feet in a traditional gesture of respect as she put a red stripe of vermilion on his forehead as a blessing, while crackers burst outside amid supporters' chants of "Modi, Modi."

Persona grata again

Narendra Modi's trajectory from a shunned regional politician accused of complicity in sectarian slaughter to a respected victor of the biggest-ever democratic vote has been followed in the UK, with David Cameron issuing an invitation to the new Indian prime minister-elect.

Britain froze links with Modi in 2002 following serious inter-community violence in Gujarat, the western Indian state where he was chief minister, in which more than 1,000 people died, many of them Muslims. Modi was accused of condoning the violence and even encouraging it – allegations he has vehemently denied. The UK cut ties with his administration, and he was later denied a US visa.

But on Friday a spokesman for Cameron said: "The prime minister called Narendra Modi this morning to congratulate him on his victory in the Indian elections and the record turnout, making this the biggest democratic election in history.

"Mr Modi said he would be delighted to accept the prime minister's invitation to visit the UK. Both leaders agreed on the importance of the UK-India relationship and agreed to work together to strengthen it in the months ahead."

Cameron also tweeted his personal congratulations, adding a desire to "work together to get the most from UK-India relationship".

The situation is unlikely to change if Labour, the party in government in 2002, re-takes office next year. Labour has previously expressed willingness to engage with the BJP leader. The Labour MP Barry Gardiner invited Modi to speak at the Commons last year – an offer the Indian politician declined.

US president Barack Obama told Modi by phone that he looked forward to working closely with him to "fulfill the extraordinary promise of the US-India strategic partnership," the White House said.

"The president invited Narendra Modi to visit Washington at a mutually agreeable time to further strengthen our bilateral relationship."

A US visit could come as soon as September, at the UN general assembly in New York.

Peter Walker and agencies