U.S. Vice President Mike Pence takes a question during a news conference in the briefing room of the White House in Washington, D.C., U.S., on Saturday, March 14, 2020.

Trump administration officials on Saturday made the clearest indication yet they expect to bring forward a third coronavirus bill aimed in part at helping industries struck by the pandemic.

President Donald Trump signed an $8.3 billion relief bill earlier this month, helping states fund their efforts to battle and contain the virus. The House passed a bill last night aimed largely at protecting individuals, offering measures like enhanced unemployment benefits, local food bank funding and paid leave.

"We got the initial support on $8.3 billion of Congress, [and] the House passed legislation to act on the president's priorities," said Vice President Mike Pence at a press conference Saturday.

"We understand the president has made clear that, whether its our airline industry or cruise line industry, we expect to be coming back to Congress."

Treasury Secretary Steven Mnuchin made assurances there was "bipartisan support" for some economic relief. Still, it is not yet clear what sorts of demands Democrats would require along with any package that supports the airline or cruise industries.

Both Mnuchin and Pence made reference to the ailing travel industry, which has been pummeled around the world with canceled trips, conferences, and cruises, as authorities have increasingly urged individuals, particularly those who are vulnerable, to avoid travel.

In some cases, the administration has added outright bans. Trump earlier this week announced that foreigners who have been in 26 European countries over the last two weeks won't be allowed in the U.S. for 30 days. Pence said Saturday that, effective midnight Monday, those restrictions will expand to the U.K. and Ireland.

It has been widely expected the government will step in to support the largest airlines if need be, because of the critical role they play in the U.S. economy. Mnuchin expressed that view Saturday.

"Airlines are the most obvious because we have a unique circumstance where we've shut down travel, and these are of strategic importance to us, but I appreciate there's many industries that are impacted by this – and I would also say that there many individuals," Mnuchin said.

In an interview Sunday with Fox News, Mnuchin was more explicit: "We're going back to the Senate this week on other things," Mnuchin said

"Airlines − very focused on airlines − hotels, cruise ships, workers for these industries," he added.

The CEOs of both United Airlines and Delta have confirmed they've been in talks with the administration about potential government aid.

"We are in discussions with the White House and Congress regarding the support they can provide to help us through this period," Delta's CEO Ed Bastian wrote to employees on Friday, announcing the largest capacity cuts in the airline's history and warning the carrier will defer aircraft and park up to 300 planes.

"I'm optimistic we will receive their support. That said, the form and value is unpredictable, and we can't put our company's future at risk waiting on aid from our government."

Other industries have also argued their case.

"Temporarily shutting off travel from Europe is going to exacerbate the already heavy impact of coronavirus on the travel industry and the 15.8 million Americans whose jobs depend on travel," wrote US Travel Association CEO Roger Dow when Trump announced the first round of European travel restrictions.

"We have and will continue to engage Congress and the administration on policy steps that are necessary to ensure that travel employers—83% of which are small businesses—can keep the lights on for their employees."

The travel and leisure industry is pushing for a number of relief measures, including tax credits for employee retention and the ability to carry back net operating losses, CNBC has reported.

The Cruise Lines International Association has highlighted its role in the U.S. economy when announcing the decision to temporarily suspend cruise ship operations.

"The cruise industry is a vital artery for the U.S. economy, supporting over 421,000 American jobs, with every 30 cruisers supporting one U.S. job, and annually contributes nearly $53 billion to the U.S. economy," it said in a statement.

"Cruise activity supports travel agencies, airlines, hotels and a broad supply chain of industries that stretches across the United States."

Pence met with cruise executives in Florida last week.

-- CNBC's Leslie Josephs contributed to this report