The president of Serbia unveiled a monument to Nikola Tesla in New York state on Monday, marking the latest milestone in a long-running campaign to raise the profile of the cult scientist and inventor around the world.

Tomislav Nikolic told the crowd at Tesla's former Wardenclyffe laboratory in Long Island that the scientist was a man whose "ideas were larger than his time", in a ceremony that also served as an opportunity for the Serbian president to remind the world of Tesla's nationality.

"The strength of Tesla's vision – because you can't forget he died more than 70 years ago – is what influences how the public speaks about Nikola Tesla: with respect," Nikolic told the Guardian, following a ceremony attended by several members of the Serbian cabinet and a large number of Serbian diaspora.

"In turn, the public will also speak about Serbia with respect."

Tesla was born in modern-day Croatia in 1856 to Serbian-Orthodox parents and went to university in Graz, Austria before becoming chief electrician for a Hungarian telephone company. He moved to Paris and then to New York in 1884, where he began to work for Thomas Edison.

The pair's relationship soon soured, however, eventually becoming a bitter rivalry. Notably, the inventors clashed over whose method of delivering electricity was more efficient and effective. Tesla's alternating current (AC) was widely adopted over Edison's direct current (DC), but Tesla never made significant money from this success and Edison remained the better-known inventor for most of the 20th century.

The unveiling of the three-quarter length statue of Tesla – showing him with arms outstretched, seemingly engaged in some sort of scientific endeavour – was not just a proud moment for the inventor's homeland, however. The Tesla Science Center had lobbied for 20 years to turn Wardenclyffe, in the tiny town of Shoreham, on the north shore of Long Island, into a museum. It finally managed to acquire the site this year, after a high profile Indiegogo campaign run by Matthew Inman, founder of the popular web-comic The Oatmeal and avid Tesla enthusiast.

Inman – described by Nikolic as an "enthusiastic young man" – was at the ceremony, and praised the "geeks" who had made the Tesla museum possible.

"Nikola Tesla was this man where [if you knew who he was] ... It was like you were in this club," Inman told the crowd of around 100 people. "I fell in love with Tesla because of his character," Inman concluded, to nods of approval. "He was a geek at heart. When I started this campaign to try and buy Wardenclyffe I think that's who funded it. People who were geeks."

The campaign – "Let's build a goddamn Nikola Tesla museum" – had aimed to raise $850,000 through the crowdfunding website Indiegogo on behalf of the Tesla Science Center. The state of New York promised to provide matching funding, which would enable the Center to buy Wardenclyffe laboratory for the asking price of $1.6m with money to spare.

The $850,000 fundraising goal was reached within days of the launch of the campaign, however, with supporters eventually contributing $1.3m. The sale was completed in May 2013, but the laboratory is not close to reopening yet. The tumultuous history of the site – including use as a dumping ground for highly toxic chemicals while it was owned by a photography company – means the project is a huge undertaking. Volunteers had worked to improve the grounds over the summer, however, and with the Tesla statue now standing at the end of a lawn looking back at the iconic laboratory the site is beginning to take shape.

On Monday the crowd huddled together on the lawn in front of the former laboratory, as a cold autumn wind blew across the site.

The ceremony began with a Serbian singer belting out a sterling rendition of The Star Spangled Banner. She barely paused for breath as she launched straight into the Serbian anthem, taking many of the Serbs in the crowd with her. Two women in traditional Serbian dress flanked the statue of Tesla as the gentle murmur of the singing drifted across the lawn.

With the monument unveiled and blessed, Nikolic and many of the crowd decamped to a private reception at the nearby Shoreham Country Club, overlooking the Long Island Sound.

After a lunch of traditional Serbian meats and cheeses, and some handing over of flags, the Guardian spoke to Nikolic on a bench overlooking the rough waters of the bay.

The president, who will attend the UN general assembly this week and had a drinks reception with Barack Obama and other heads of state planned for Monday night, was unabashed about his hopes that Tesla becoming more recognised could also serve as a boon for Serbia.

"I am convinced that the standing of Nikola Tesla – as well as the standing of some contemporary Serbs who are achieving great things – has hugely aided Serbia's image [internationally]," Nikolic said. "I look at that image today, compared to a year ago – not to mention 20-or-more years ago – and I see a world of difference."

The president admitted that he had initially been lobbying for the Tesla statue to be placed in front of the United Nations, rather than the Wardenclyffe laboratory site.

"I thought the statue should sit in a location where thousands of people pass by daily to see it," Nikolic said. However, "once the Wardenclyffe land was bought, it was surely the right idea to establish this monument here," he added.