The standards chief of the US Congress says a senior Trump aide was "wrong, wrong, wrong" to promote Ivanka Trump products on live television.
Jason Chaffetz, a Republican who heads the oversight committee in Congress, said the promotion was "clearly over the line, unacceptable".
Trump aide Kellyanne Conway had said on Fox News: "Go buy Ivanka's stuff."
Her comment came after retailer Nordstrom dropped Ivanka's clothing line, citing a lack of sales.
In response, President Donald Trump tweeted to say his daughter had been treated "so unfairly" by the retailer.
The White House said on Thursday that the president "absolutely" continued to support Ms Conway, despite intense criticism of her remark by politicians.
On Friday morning, Ms Conway tweeted: "POTUS supports me, and millions of Americans support him & his agenda."
Federal ethics rules prevent White House employees giving an "endorsement of any product, service or enterprise".
Mr Chaffetz said the White House should notify the Office of Government Ethics so it could initiate an inquiry. There have been numerous concerns over possible conflicts of interest for White House staff.
He said he and his Democratic counterpart would write to Mr Trump.
"It needs to be dealt with," he told the Associated Press. "There's no ifs, ands or buts about it."
What's the context?
Nordstrom became the fifth retailer to drop the Ivanka Trump clothing line, citing lack of sales.
The move comes amid a boycott of all Trump products, which activists have dubbed #GrabYourWallet, in reference to a 2005 comment Mr Trump made about women's bodies.
Nordstrom said the decision was based on the brand's performance, which is what the firm repeated on Wednesday.
"Sales of the brand have steadily declined to the point where it didn't make good business sense for us to continue with the line for now," the company said in a statement, adding that Ivanka Trump was personally informed of the decision in early January.
However, in a tweet on Wednesday, the president attacked the company, saying: "My daughter Ivanka has been treated so unfairly by Nordstrom. She is a great person - always pushing me to do the right thing! Terrible!"
The tweet, which was sent by Mr Trump's @realDonaldTrump account, was then retweeted by the official @POTUS account.
Shares in the retailer briefly fell 0.7%, before rising later in the day.
Ivanka Trump does not have a fixed role in the White House, but has been a regular fixture since her father's inauguration. Her husband, Jared Kushner, is a key Trump adviser. Ivanka Trump gave up operating control - but not ownership - of her businesses after her father's election.
What did Kellyanne Conway say?
"Go buy Ivanka's stuff," Ms Conway told the Fox and Friends show in an interview from the White House briefing room. "I'm going to go get some myself today. I'm going to give a free commercial here: Go buy it today, everybody."
Her comments came only days after she was lampooned for citing the "Bowling Green massacre", which never happened, while trying to justify the president's controversial immigration ban.
Analysis: Anthony Zurcher, BBC North America reporter
Kellyanne Conway is definitely in hot water. Her comments about buying Ivanka Trump clothing - seemingly a light aside at the end of a television interview - are being treated as no joking matter by angry Democrats, concerned government watchdogs and even some in her own party.
Traditionally, this would be a matter handled by supervisory staff, with discipline possibly including reprimands and docked pay. Complicating the situation in this case is that the Trump White House itself would be responsible for imposing the sanctions.
Ms Conway has been the very public face of the Trump administration and the Trump campaign before it. She has earned the trust of the president as an aide of unquestioned loyalty. Will the president be willing to punish such a transgression?
This also raises the possibility of a strategic benefit to Ms Conway's involvement in this growing conflagration. Like a destroyer taking a torpedo to save an aircraft carrier, she has deflected the political blast from the Nordstrom controversy away from her president, whose questionable tweet set everything off.
While Ms Conway's remarks were ill-advised and very likely a violation of the law, Mr Trump's use of presidential power to protect his family's business interest is of greater national concern.
What has been the response?
White House press secretary Sean Spicer said Ms Conway had been "counselled" after her remarks.
But according to the Associated Press, Mr Trump was unhappy with Mr Spicer's use of the word "counselled", because he felt it made it sound as though she was in trouble.
But the calls for further investigation or sanctions are growing. "It's a violation of the rule," Norman Eisen, a former ethics adviser to Barack Obama, told MSNBC. "It's a serious matter."
Two liberal lobby groups have filed complaints with the Office of Government Ethics.
"Conway's action reflects an ongoing careless disregard of the conflicts of interest laws and regulations by some members of the Trump family and Trump administration," Craig Holman, government affairs lobbyist for one group, Public Citizen, told AP.