House Speaker Paul D. Ryan (R-Wis.). (Allison Shelley/Getty Images)

House Speaker Paul D. Ryan is calling on the administration to start talking to the United Kingdom about a new trade agreement to ensure “a smooth” relationship after the country parts ways with the European Union.

But other key Republicans are urging patience while the complicated Brexit process unfolds.

Republicans have been wrestling with how to respond — particularly on the issue of trade — to last week’s referendum in which British voters decided to leave the E.U. American voters in both parties registered their anti-trade sentiment during this year’s presidential primaries, and Donald Trump delivered a fiery speech Tuesday night vowing to rip up trade deals as president.

[Trump trashes trade deals and advocates tariffs]

Ryan (R-Wis.) advocates being aggressive early in establishing deals with Britain.

“Obviously it takes time to do something like this, but I think it is something we should be working on,” Ryan told ABC affiliate WISN in Wisconsin last week, according to comments his office published on the speaker’s website Monday. “We should begin discussions with Great Britain to ease concerns so that we do have a smooth trade relationship with Great Britain, because they are our indispensable ally.”

Ryan later added on Wisconsin radio station WBEL that negotiations with Britain should be done on “a parallel track” to ongoing talks with the E.U. toward a trade agreement known as the Transatlantic Trade and Investment Partnership, or TTIP.

Ryan, a frequent champion of free trade as a tool to improve foreign relations, isn’t the only lawmaker urging the administration to launch talks with London to ensure the U.S.-U.K. relationship won’t be harmed by British-European divorce proceedings.

Sen. Tom Cotton (R-Ark.) said in a statement Friday soon after the Brexit results were announced that talks should begin now.

Sen. Mike Lee (R-Utah) announced Friday that he would introduce legislation that would require the United States and Britain to “honor our current arrangements” until new bilateral deals are drafted. It also would direct the U.S. trade representative to begin negotiations “as soon as possible.”

But on Tuesday, other Republicans urged more patience before the United States dives into negotiating a new deal.

“It’s going to take some time for them to figure out their transition exit from the E.U.,” said Sen. John Thune (R-S.D.), a member of the Senate GOP’s leadership team and the Finance Committee, which has jurisdiction over trade issues. “Until that happens, I think it’s probably going to be difficult for us to weigh in there.”

Thune also pointed out that it would be hard for the United States to negotiate a trade deal with London until Washington has a better sense of what Britain’s trade relationship with the E.U. will be post-split.

“I think we should wait and see how it shakes out,” said Sen. Rob Portman (R-Ohio), stressing the same uncertainty.

Portman, who is a Finance Committee member and served as U.S. trade representative in the George W. Bush administration, also cautioned against trying to separate talks with Britain from ongoing trade talks with the E.U.

“We need [Britain] to help us influence the rest of Europe to be open to our products,” Portman said, pointing out that Britain was “less protectionist” than many European countries and has been “a relatively positive force” in negotiating with Europe.

It is the administration’s job to negotiate trade deals and then submit them to Congress for approval. Last year, Congress renewed “fast track” authority, which establishes a procedure under which Congress cannot amend the agreements and can approve trade deals with a simple majority.

Since then, however, lawmakers in both parties have expressed skepticism about approving the pending 12-nation Trans-Pacific Partnership agreement as the electorate’s mood toward trade deals has soured. It’s not clear when Congress will vote on the deal, but it almost certainly will have to wait until after the election.

Any new deals struck with Britain would almost certainly have to be considered by the next president and a future Congress.

Britain is not expected to formally commence withdrawal proceedings until after a prime minister is chosen to replace David Cameron, something that may not happen until September. And Britain and the E.U. have two years after Britain formally commences that process to negotiate the final terms of their separation.

There are some questions about whether Britain will even get to that point; millions of Britons have petitioned the government for a second referendum — although a second vote is unlikely at this point.

Democrats seemed uninterested in jumping into new trade negotiations until more of these uncertainties surrounding Brexit are ironed out.

“I think we’ve got to let the dust settle before we decide anything because of Europe,” said Sen. Charles Schumer (D-N.Y.), who sits on the Finance Committee.

Sen. Sherrod Brown (D-Ohio), also a committee member, said: “It’s too early to tell if we do separate trade agreements. I don’t even know what that means yet.”

David Weigel contributed to this report.