The Brexit has prompted congressional Republicans to press for a bilateral trade agreement with the U.K., a subtle rebuke of President Barack Obama, who said before the vote that the U.K. would move to the “back of the queue” for a trade deal.

Last week, House Ways and Means Committee Chairman Kevin Brady (R., Texas), whose panel oversees trade policy, said that the U.S. should begin to discuss “a modern, new trade agreement” with the U.K. to continue and expand trade between the two nations. On Thursday, Rep. Charlie Dent (R., Pa.) went a step further and said he would introduce a resolution to urge the Obama administration to begin talks on establishing a bilateral trade agreement with the U.K. now that the country has voted to leave the European Union.

“The Brexit referendum, for better or for worse, is behind us,” Mr. Dent, a member of the House Appropriations Committee’s subcommittee that focuses on foreign operations, said in a statement. “Now Congress has a responsibility and interest to work with the United Kingdom, particularly when it comes to strengthening economic ties between our two great nations.”

Mr. Dent said the resolution would call on the White House to direct the U.S. Trade Representative to immediately begin discussions for a U.S.-U.K. bilateral trade agreement.

On Wednesday, Mr. Obama said that the U.K.’s trade relationship with the U.S. would “be the least of their concerns because their first order of business is going to be to address the market where they sell half their goods.” He emphasized that “the special relationship that we have with Great Britain does not change.”

The vote last week to leave the EU carries consequences for the U.K. economy. Leaders of the 27 remaining states have said the U.K. wouldn’t be able to gain access to the single market of goods and services unless it shared some of the obligations of membership. The U.K. still must formally disentangle itself from Europe.

A resolution would underscore the longstanding special relationship between the U.S. and the U.K. A bust of former British Prime Minister Winston Churchill sits just outside the entrance to the House speaker’s office. Congress is full of Anglophiles like Mr. Dent who are intent on preserving that relationship.

It would also mark a contrast with the approach of the White House, which has urged a slow process for the U.K.’s exit from the EU and has pressed the remaining 27 members to address the concerns that led to the referendum and risk prompting a cascade of similar votes across Europe.

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