The dollar edged up on Tuesday after news that a new poll on Britain's referendum on European Union membership showed growing support for the "Leave" camp, pushing down the euro and sterling.

The dollar rose to a session high against a basket of six currencies after polling firm Survation showed the percentage of voters supporting Britain's exit from the EU had risen to 44% from 42% in its previous poll on Sunday. A majority of respondents still preferred "Remain," but by just a 1 point margin, with 45 percent support.

The dollar index  rose 0.25%  to 93.824 after earlier being flat.

Investors had kept the dollar constrained ahead of testimony from Federal Reserve Chair Janet Yellen to the U.S. Senate Banking Committee, a speech by European Central Bank chief Mario Draghi and further results from 'Brexit' polling later in the day.

Sterling turned negative against the dollar after the poll's release, but remained above session lows. It fell to $1.4675. It reversed those losses, however, and turned positive.

Two earlier opinion polls on Monday indicated the "Remain" camp has regained some ground before the June 23 referendum. However, a third poll found the "Leave" campaign ahead by a hair. 

Sterling had climbed to $1.4788, its highest since early January against the dollar in European trading after the release of the earlier opinion polls. 

The euro fell 0.4% to a session low of $1.1266.