By Stephen Evans BBC North America business correspondent

It is understood that the US accepts that the dollar should not get much weaker against the yen and the euro.

The Americans also want the Chinese currency to be able to move more freely according to the market's dictates.

The call was made in a statement at the end of the two-day meeting in a luxury resort on Florida's Atlantic coast.

The final statement was broad: the global economic recovery has strengthened significantly, it says.

The dollar looks set to stay weak

There should be renewed attempts to bring freer trade.

Excess volatility and disorderly movements in exchange rates are undesirable.

The sub-text of this last assertion is that there is behind-the-scenes agreement that the dollar has fallen enough against the pound, the yen and the euro but that the Chinese currency should be allowed to move more freely.

The Chinese Government currently intervenes so it shadows the dollar.

Oddly perhaps, the Chinese are not part of G7.

Whatever accord is reached though, there is one big political reality - this is election year in America and a weak dollar suits Mr Bush because it promotes American exports and so growth in an economy which will be a hot issue at the polls in November.

This means that there is unlikely to be any stark change of policy until after the election.

The dollar is weak then, it probably will not fall much further but nor will it rise. Or so finance ministers intend.