Senator Ben Sasse, " Republican of Nebraska, said that it was "good-news" which the president had directed his economic advisor, Larry Kudlow, and his trade, Robert Lighthizer, to explore re-joining the offer.
Sen. John Thune (R-S.D.) said that he and others at the table raised the point that "if you really want to get China's attention, one way to do it is start doing business with all the people they're doing business with in the region: their competitors".
The move could mark the beginning of a stunning shift for Trump, who railed against the Trans-Pacific Partnership during the campaign and made withdrawal from the pact a priority during his first week in office.
An agreement could be completed within a few weeks or five months, he said, adding "I don't care".
President Donald Trump listens as he meets with the Emir of Qatar Sheikh Tamim bin Hamad al-Thani in the Oval Office of the White House, Tuesday, April 10, 2018, in Washington.
On talks with Canada and Mexico to revamp Nafta, Trump said negotiations are "coming along great", though he added there's no timeline on reaching a deal.
Rejoining the pact would be a major reversal as Trump escalates a trade conflict with China. He says that's shifting work to competitors outside the U.S.
The agreement never went into effect, however, because Trump withdrew from it three days after he was sworn in.
It's unclear how willing the other 11 countries would be to reopen the agreement and make concessions to lure the United States back, though its economic power would likely be an appeal.
"I have to believe President Xi is smiling all the way to regional domination as a result of our pulling out of TPP". It's a harsh word - it's a rape of our country. "He's going to get rid of a lot of taxes and tariffs", Trump said of Xi.
The president says China has consistently treated US agriculture unfairly and his administration is "changing things with respect to trade". In fact, in February, a letter from 25 congressional Republicans had been delivered to Trump asking that he "re-engage" with the TPP. A trade war with China could be particularly devastating to rural economies, especially for pig farmers and soybean and corn growers.
Kevin Kennedy, president of a steel fabrication business in Texas, said tariffs on steel and aluminum imports have led USA steel producers to raise their prices by 40 percent. Sen Ron Johnson, R-Wis., was among a handful of senators who recently visited China to meet with government and business leaders there.
In February, Treasury Secretary Steven Mnuchin said the US was interested in reentering the trade agreement, but he quickly backed off those comments, making it sound like a deal would not materialize.
Eleven other Pacific Rim countries signed a sweeping trade agreement last month that came together after the USA pulled out.
The countries signed the agreement but they still must individually ratify it before it can be formally implemented.