Tony Blair addressed an audience of top Republicans during a two-day strategy retreat held by the party in the town of Hershey, Pennsylvania, hours before David Cameron was due to arrive in Washington.

The former British prime minister was speaking at a lunch discussing “the Middle East peace process, as well as issues relating to the wider region, in his capacity as Quartet Representative”, according to his spokesperson.

A source inside the closed-door lunch on Thursday said that Blair was well-received by those in the room, some of whom had made the trip just to see him.

Blair was not paid for attending, although he did receive travel expenses.

Tucker Eskew, a Republican strategist who worked in Downing Street as president George W Bush’s wartime communications representative, said Blair’s reputation in America benefited from a sense that he stood for a more historic alliance between the two countries.

“We have a different perspective and the benefit of distance and time,” he said.

“My Blairite friends would perhaps not thank me for saying this, but Republicans find in Blair some of the same qualities that they found in prime minister Thatcher. Although there are plenty of Democrats who would feel differently [about a speech from Blair] because to them it would all be about the wars in Iraq and Afghanistan, to us this is about a deeper history.”

Top of the list at the party meeting is their opposition to Obama’s environmental policy – a stance that runs so deep that Democrats plan a vote next week to see if any senate Republicans will admit to believing in man-made climate change at all. They were also pushed to explain their opposition to recent White House plans for limited new maternity leave that would look positively libertarian in a British political context.

Not everybody in the Republican party has entirely forgotten or forgiven the Iraq and Afghan wars that have made Blair and president George W Bush such pariahs on the international stage, but the party’s private retreat is perhaps one of the last major political arenas where an audience is prepared to overlook that uncomfortable chapter.

After years of fighting Obama, Republicans are also in more conciliatory mood as they assume power in Congress and try to appeal to moderates in the 2016 race for the White House. A British Labour politician who can make the ideological journey all the way to the conservative heartland without so much as blushing may be the flexible role model the party is looking for.

Blair’s presence will not have gone unnoticed at the White House, where Obama is under pressure to show he has not lost touch with his British ally in the process of pulling both countries out of the painful entanglements in Iraq and Afghanistan.

But Democrats, who are holding their own strategy retreat at the same time in Baltimore, may draw some comfort from the fact that Blair’s presence also served as a ploy to encourage Republican senators and congressmen to put their usual rivalry aside.

What is less clear is whether it was Blair who received top billing, or the other celebrity also addressing the meeting to boost the turn out: retired television host and comic Jay Leno.

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