WASHINGTON—At the request of President Donald Trump’s son-in-law, Jared Kushner, and his wife, Ivanka Trump, language critical of a global climate deal was struck from an executive order that Mr. Trump is planning to sign soon, according to multiple people familiar with the move.

Mr. Trump is expected to sign within days at least two executive orders that will begin the process of trying to dismantle former President Barack Obama’s climate and environmental regulations.

Mr. Kushner, a senior adviser to Mr. Trump, and Ms. Trump, the president’s eldest daughter, intervened to strike language about the climate deal from an earlier draft of the executive order, according to these people.

The executive order, which targets Mr. Obama’s broad climate agenda, now includes no mention of the climate deal, which nearly 200 nations struck in Paris in 2015, in large part due to a strong push by the Mr. Obama’s administration.

One White House official said both Mr. Kushner and Ms. Trump have been considered a moderating influence on the White House’s position on climate change and environmental issues. The move is the latest sign of influence Mr. Trump’s daughter and Mr. Kushner have in a White House that has seen internal divisions on a variety of issues, including foreign policy.