Barack Obama was caught between two competing European visions of how to solve the financial crisis at the G8 summit when David Cameron rejected outright a French proposal to raise €57bn (£46bn) through a tax on financial transactions.

The eurozone crisis is set to dominate four days of intense diplomacy which began in Washington Friday morning and continued through a meeting of G8 leaders at the presidential retreat Camp David on Friday evening. Discussions will continue there on Saturday and on to a Nato meeting in Chicago.

In talks at the White House, only hours before the Camp David summit, Obama met the new French president, François Hollande, for a one-to-one conversation in which he explored the possibility of a new approach to the eurozone crisis based on a pro-growth, stimulus strategy. Obama has been pressing for such a strategy for the past three years and has a potential ally in Hollande.

The White House welcomed what it sees as a change in the debate since Hollande's election that tilts the balance slightly more in favour of a growth strategy.

The French president is proposing an EU-wide financial transaction tax (FTT) that could raise up to €57bn a year that could be used to stimulate the 27-nation bloc.

After meeting Obama, Hollande was scheduled to meet David Cameron in Washington before flying to Camp David.

However on arriving in the US, Cameron said: "On the financial transactions tax I'm very clear. We are not going to get growth in Europe or Britain by introducing a new tax that would actually hit people as well as financial institutions. I don't think it is a sensible measure. I will not support it."

Cameron pointedly backed Hollande's conservative rival, Nicolas Sarkozy, in the presidential election and refused to meet Hollande in London during the campaign. However, the prime minister has now been trying to forge an alliance with the new French government to press Germany to do more to solve the euro crisis. The FTT is proving a sticking point between them.

In his meeting with Obama, Hollande hinted at a compromise over his election pledge to pull French combat troops out of Afghanistan early. The US and Britain fear a premature exit by France could also send other countries rushing to the exit ahead of the 2014 deadline for withdrawal.

At the White House, Hollande insisted he was standing by his pledge but left the door open for a compromise. He said he was committed to providing assistance on Afghan security but in a different way and this would be discussed at the Nato summit held in Chicago on Sunday and Monday. It is thought Hollande and Obama discussed French troops switching to a training role.

Obama was looking for a good relationship with Hollande, hoping to enlist him as an ally in support of the US push for a pro-growth/stimulus approach to the eurozone crisis.

The two appeared to get along, with Obama teasing Hollande about having studied fast food. Hollande said he had nothing against "cheeseburgers", prompting Obama to add lamely that cheeseburgers "go very good with French fries".

The G8 leaders were set to discuss national security issues such as Syria and Iran over dinner and aid for the developing world in the morning. But the bulk of the time was being devoted to the European crisis.

It is the first time a US president has gathered so many leaders at the relatively small Camp David venue. Most meetings normally involve invitations to just one or two others. With space at a premium, each of the G8 leaders has been assigned a cabin and they will gather for discussions around a communal dining table.

As well as Hollande, Cameron and Germany's Angela Merkel, there will be Canada's prime minister, Stephen Harper, the Italian prime minister, Mario Monti, the Japanese prime minister, Yoshihiko Noda, and the Russian prime minister, Dmitri Medvedev, who is attending in place of the Russian president, Vladimir Putin.

Although there is little motivation in either the G8 or Nato for military intervention in Syria, Cameron is to call for more military observers to be sent to Syria. He is offering to send a senior Ministry of Defence official at colonel rank to act as chief of staff to General Robert Mood, the chief military observer at the UN supervision mission in Syria.

In a speech in Washington that kicked off the weekend of diplomacy, Obama announced $3bn (£2bn) in new money to help tackle hunger, mainly projects to help small farmers in Africa. Crucially, however, the cash is to come from the private sector. There has been no announcement yet about whether there will be any funds from the G8 countries on top of the $22bn they committed in 2009 to deal with hunger over the following three years.

Obama said it was important the G8 focused on "the urgent challenge that confronts some 1 billion men, women and children around the world – the injustice of chronic hunger". He added: "As the wealthiest nation on earth, I believe the United States has a moral obligation to lead the fight against hunger and malnutrition, and to partner with others."

Oxfam expressed concern that Obama's announcement "focuses too heavily on the role of the private sector to tackle the complex challenges of food insecurity in the developing world". It called on the G8 to commit substantial funds.