The Commerce Department barred ZTE in April from importing American components for seven years after concluding that the company deceived US regulators after settling charges last year of sanctions violations.
Once the bill leaves committee, President Trump must either sign it into law or veto it.
"We've articulated our desire to better educate members about the ZTE action by Commerce, and we expect to address it in conference", White House legislative liaison Marc Short said last week."We think we can fix it in conference", Short added, referring to the process when differences in House and Senate bills are reconciled.
In a rare departure from White House policy, the Republican-led Senate passed the NDAA on Monday that included two provisions that prevent any federal official from removing penalties on ZTE.More news: Cristiano Ronaldo overtakes Ferenc Puskas' global goal record
More news: Protest held at Courthouse in opposition to Trump administration's border actions
More news: YouTube rebrands Red to Premium, announces European launches
The administration announced an agreement with ZTE earlier this month but has run into opposition in Congress. It includes several measures aimed at Chinese telecom and surveillance equipment firms-including one that directly defies a recent Trump decision to throw a lifeline to crippled Chinese telecom firm ZTE.
In a joint statement, Senators Marco Rubio, Chuck Schumer, Chris Van Hollen, and Tom Cotton said: "We're heartened that both parties made it clear that protecting American jobs and national security must come first when making deals with countries like China, which has a history of having little regard for either". The company has lost almost two-thirds of its value since it resumed trading last week after a two-month suspension that followed the initial ban.
Commerce banned ZTE from buying American parts-including Qualcomm computer chips-that it depends on to manufacture its products.
The Senate NDAA also includes an amendment prohibiting sales to Turkey of F-35 Joint Strike Fighter jets made by Lockheed Martin Corp unless Trump certifies Turkey is not threatening North Atlantic Treaty Organisation, purchasing defense equipment from Russian Federation or detaining USA citizens.
White House spokeswoman Lindsay Walters had said the meeting would focus on the "problematic" amendment to the defense bill, but the gathering ended up largely addressing an ongoing furor about the Trump administration's policy of separating migrant children from their parents at the US border.