WASHINGTON >> President Donald Trump offered a measured gesture of support for the embattled head of the Environmental Protect Agency today but those words of encouragement for Scott Pruitt also came with a White House warning about the ethical questions surrounding his travel spending and ties to Washington lobbyists.

“I hope he’s going to be great,” Trump told reporters, declining to reiterate publicly his private praise for Pruitt’s work.

In a phone call Monday, Trump told the EPA chief “we’ve got your back” and urged him to “keep his head up” and “keep fighting,” according to two administration officials. The officials spoke on the condition of anonymity because they were not authorized to discuss private conversations publicly.

But two other officials, also without authority to be identified, said the praise referred to Pruitt’s work in loosening environmental regulations that the Trump administration has argued hamstring manufacturers and in provoking blowback from environmental groups.

Those officials added that the call’s tone was not entirely positive — and that the White House is displeased by the cloud over Pruitt. They also said John Kelly, Trump’s chief of staff, delivered a warning to Pruitt about the White House’s displeasure.

Trump has repeatedly offered praise for embattled members of his administration, even while privately plotting their ouster and interviewing replacements.

Meanwhile, two Republicans representing left-leaning South Florida districts, Reps. Carlos Curbelo and Ileana Ros-Lehtinen, joined Democrats and environmental groups today in calling on Pruitt to resign or be fired.

In a tweet, Curbelo said Pruitt’s “corruption scandals are an embarrassment to the Administration, and his conduct is grossly disrespectful to American taxpayers.”

The White House has grown weary in recent weeks of the scrutiny of administration staffing after a wave of departures — some voluntary and others forced — weakened morale.

Pruitt was one of several Cabinet officials summoned a month ago to meet with White House lawyers and Cabinet affairs staff over ethical questions, where they were warned that further negative headlines could imperil their jobs. Officials said he did not disclose his housing situation to at the time.

Pruitt has come under intense scrutiny for his use of a Capitol Hill condominium owned by the wife of prominent Washington lobbyist Steven Hart, whose firm represents fossil fuel companies. An agency ethics official at the EPA has insisted that Pruitt’s lease didn’t violate federal ethics rules.

A memo signed by Kevin Minoli contends that Pruitt’s $50-a-night rental payments constitute a fair market rate. Pruitt’s lease, however, required him to pay just for nights he occupied in the unit. Pruitt actually paid a total of $6,100 over the six-month period he leased the condo, an average of about $1,000 a month.

But current rental listings for two-bedroom apartments in the neighborhood show they typically go for far more than what Pruitt paid. A two-bedroom townhome on the same block as the one leased by Pruitt was advertised for rent on Monday at $3,750 a month.

Records show that while Pruitt was living in the condo, he met in his EPA office with a lobbyist from Hart’s firm and two executives from an energy company seeking to scuttle tighter pollution standards for coal-fired power plants. EPA also granted a favorable ruling to a pipeline company also represented by Hart’s firm.

Walter Shaub, who ran the U.S. Office of Government Ethics until resigning last year, tweeted that EPA’s legal justification of Pruitt’s living arrangements was “Total Baloney.”

Democrats from both the House and Senate issued letters today urging the EPA’s inspector general to investigate Pruitt’s living arrangements. Spokeswoman Jennifer Kaplan said the watchdog office is evaluating the requests. It is already probing Pruitt’s outsized 2017 travel spending, which has included extensive use of bodyguards and frequent use of first-class airline tickets. Though federal regulations typically require federal officials to fly in coach, the EPA chief has said he needed to sit in premium seats due to security concerns.

A Republican who previously served as the state attorney general of Oklahoma, Pruitt has long been a champion of the oil and gas industry. In the year he has served as the Trump administration’s top environmental official, Pruitt has moved to scrap, gut or replace numerous environmental regulations opposed by the industry while boosting the continued burning of fossil fuels, which is the primary cause of climate change.

Trump is said to be fond of Pruitt and has cheered his moves to rollback regulations and do battle with environmental groups.

The president’s call to Pruitt came just days after another Cabinet official, Veterans Affairs head David Shulkin, was dismissed after stirring ethics concerns. An inspector general’s report concluded that Shulkin had inappropriately accepted Wimbledon tickets and his staff had doctored email to improperly justify free travel for his wife. Shulkin denied any wrongdoing.

Other Trump Cabinet members, including Housing Secretary Ben Carson and Interior head Ryan Zinke have also faced questions about their expenditures. Last year, Trump’s first health and human services secretary, Tom Price, was forced to resign over concerns about private air travel on the government’s dime.