Sen. John Cornyn John CornynBipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection Airline job cuts loom in battleground states MORE (R-Texas) said he is "optimistic" that President Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE will keep the U.S. in the North American Free Trade Agreement (NAFTA) after a White House meeting with Senate committees on Wednesday.

Cornyn said he is "more optimistic" that Trump won't scrap the 24-year-old trade deal with Canada and Mexico after the meeting.

"We just encouraged him to continue to modernize NAFTA," Cornyn said, according to Reuters.

Cornyn, the No. 2 Republican in the Senate, also noted that Trump was "very aware of the election in Mexico and not wanting to have an untoward effect on that."

The Wednesday meeting with members of the Senate Finance Committee came after Trump said in his State of the Union address last week that the best deal for the U.S. could mean withdrawing from the trade pact. Following the speech, 36 senators called for Trump to stay in the deal.

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Lawmakers concerned about lasting damage to the U.S. economy outside NAFTA at the meeting urged Trump to not follow through on his threats to pull out and instead to continue to negotiate to modernize the deal.

"In our meeting, we underscored that preserving NAFTA is vital for the millions of Americans whose jobs depend on trade in North America, and that weakening the agreement would jeopardize American economic growth,” said Finance Committee Chairman Sen. Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah).

Cornyn underscored the importance of making progress in negotiations with the partner countries in upcoming weeks for a successful deal, as negotiators are meeting for the sixth of seven rounds of talks.