Newer EU members say they have waited too long for an EU-wide deal
Two more EU member states have made bilateral agreements on visa-free travel to the US, a day before talks on securing a deal for the whole EU bloc.
US Secretary for Homeland Security Michael Chertoff signed memorandums of understanding in Estonia and Latvia.
A similar accord was signed last month by the Czechs, who complained that the EU had taken too long to reach a deal.
But an EU official said the memorandums had no legal standing and he said governments "should be more patient".
Most people in Western Europe can travel without a visa to the United States but citizens from other EU member states, particularly those which joined the bloc since 2004, cannot.
Although individual governments are allowed to negotiate bilateral deals on security issues such as sky marshals and secret services, visa requirements are a matter for the EU as a whole.
Mr Chertoff told reporters in the Latvian capital, Riga, that the US had the "utmost respect for EU law".
VISA-FREE TRAVEL TO US
Ireland, Portugal, Austria, Italy
Belgium, Slovenia, Denmark, Luxembourg
Spain, Finland, Sweden, France
Netherlands, Germany, United Kingdom
A European Commission spokesman said that if the accords were similar to the Czech deal, then they were likely to be acceptable.
Commission Vice-President Franco Frattini has said he hopes to discuss a "European common approach" with Mr Chertoff in Slovenia on Thursday.
But Latvian Foreign Minister Maris Riekstins said he did not see why his country should wait.
"We have not gone against any of our commitments to the EU", he said.
Hungary, Lithuania and Slovakia are expected to sign separate deals with Mr Chertoff on Friday.