The political TV advertisement featuring Binyamin Netanyahu and the slogan "The world needs American strength, not apologies" is likely to fuel claims that the Israeli prime minister is interfering in the US presidential election in support of Republican candidate Mitt Romney.

It comes increasing during anxiety that Netanyahu has overplayed his hand in displays of warmth and enthusiasm for Romney while his relationship with Barack Obama grows more antagonistic. Some say Netanyahu is gambling too heavily on a Romney victory on November 6 and that if Obama is re-elected, the potential blowback could be damaging not just for the prime minister but for Israel itself.

Mark Regev, Netanyahu's spokesman, said the advertisement had "not been co-ordinated with us, we were not consulted and no one asked us for our permission". In an interview last week with the Jerusalem Post, the Israeli prime minister rejected accusations of interference in the election, saying they were "completely groundless".

But, according to Yossi Verter writing in Haaretz recently, US officials had relayed to a "very senior Israeli figure" that "in the eyes of the Democratic administration, Netanyahu is perceived as campaigning on behalf of Mitt Romney." To the president and his aides, the Israeli prime minister's actions look like "crude, vulgar and unrestrained intervention in the US election campaign".

Joe Klein of Time magazine described Netanyahu's recent behaviour as "an unprecedented attempt by a putative American ally to influence a US presidential campaign".

The editor of the New Yorker, David Remnick, said Netanyahu seemed "determined, more than ever, to alienate the president of the United States and, as an ally of Mitt Romney's campaign, to make himself a factor in the 2012 election".

Netanyahu's categoric denial of interference followed a leak by Israeli officials that Obama had declined to meet the Israeli prime minister during his visit to the US later this month. US officials denied there had been a deliberate rebuff. Some observers believed the story was planted by Netanyahu aides in order to show the president in a poor light for snubbing the leader of one of America's closest allies.

The Israeli leader's fury with Obama appeared to reach a new level after his failed attempt to use the US election to bounce the president into setting clear "red lines" beyond which America will take military action against Iran's nuclear programme. In a press conference – from which footage was taken for the television advertisement – Netanyahu said without red lines, there could be no US-imposed red light to military action.

In contrast, Romney has indicated that an administration led by him would take a more hawkish stance. His chief aide, Dan Senor, hinted that Romney as president would back a unilateral Israeli military strike on Iran.

In July, Netanyahu warmly welcomed Romney to Israel along with his chief financial backer Sheldon Adelson, who is also a staunch supporter of the Israeli prime minister. The billionaire Adelson owns Israel Hayom, a free newspaper which invariably backs Netanyahu and his rightwing coalition government.

During his visit, Romney said: "I would treat Israel like the friend and ally it is … I cannot imagine going to the United Nations, as Obama did, and criticising Israel in front of the world. You don't criticise your allies in public to achieve the applause of your foes. If there were places where we disagree, I would hold these disagreements in private conversations, not in public forums."

Romney and Netanyahu also appear to share a common view on the Israeli-Palestinian conflict, which is to maintain the status quo rather than advance towards an independent state for the Palestinian people. In remarks secretly filmed in May and released this week, the Republican candidate said: "This is going to remain an unsolved problem … We sort of live with it." This reflects Netanyahu's approach towards the so-called peace process since his election in March 2009.

The rapport between the two rightwing politicians dates back to the 1970s when they both worked at the Boston Consulting Group.