Updated at 7:07 p.m. ET

President Trump vowed to sign the latest coronavirus relief legislation nearing the finish line in Washington on Tuesday after it was passed by the Senate.

Members of Congress have reached an agreement on about $484 billion more in relief funding to help small businesses and others hurt by the mitigation measures aimed at slowing the spread of the virus.

The House could vote as soon as Wednesday.

Trump and his aides also support more stimulus that could go far beyond crisis relief and into what Trump said he hopes is major investments in infrastructure.

Trump also said on Tuesday that he'd agreed with New York Gov. Andrew Cuomo that the Navy hospital ship USNS Comfort — which had deployed to New York City to provide surge treatment capacity for the pandemic — could return to its berth in Norfolk, Va., at the earliest opportunity.

Cuomo and Trump also said they've established that New York has enough ventilators to meet its needs and that some of them can be sent to Massachusetts or elsewhere as needed, Trump said.

Trump and his top lieutenants, meanwhile, are still fighting a number of skirmishes over federalism and the dividing line between the power of the president and the powers of the states.

Immigration executive order

Trump confirmed he plans to sign a pending executive orderthat will "temporarily suspend" immigration into the United States for 60 days, putting a stop to the issuance of green cards. The policy will not apply to temporary workers, Trump said.

The order follows years of hard-line policy by Trump on immigration and what he calls the importance of borders.

The president said on Tuesday that his goal is to keep immigrants from becoming citizens and applying for jobs that have been vacated by Americans laid off during the pandemic.

"We must first take care of the American worker," Trump said.

It wasn't immediately clear how many newcomers might have contended for the posts from which Americans have been laid off, especially given the nudge from the government for employers not to terminate workers.

Congress and the Treasury Department have tried to create incentives for employers to keep workers on payrolls with forgivable loans and other support in the trillions of dollars of relief authorized by Washington.

Treasury Secretary Steven Mnuchin said on Tuesday that he estimated 30 million American jobs have been saved thanks to paycheck support, small-business loans and other programs.

More such outflows of cash are pending from Washington in the legislation passed on Tuesday by the Senate and then in another round that Trump and Mnuchin said they hope focuses on infrastructure, especially rural broadband network capacity.

Trump's push-and-pull with governors continues

Trump and Cuomo said separately on Tuesday that their meeting was productive, and Trump suggested they'd reached some kind of accord on increasing COVID-19 testing for New York. The details weren't clear.

Trump also said he planned to talk on the phone Tuesday with Georgia Gov. Brian Kemp, who has said many types of businesses, including gyms and hair salons, may open before federal virus mitigation guidelines expire on May 1.

Trump said that he supported Kemp and that the decision was the governor's, but the president also said he wanted to learn more in the phone call scheduled for the two leaders.

Trump has fought, patched up and resumed feuds with a number of governors in both parties throughout the crisis.

Another of Trump's newer antagonists includes Maryland's Republican governor, Larry Hogan, who ordered 500,000 coronavirus tests from South Korea after concluding there was insufficient testing capacity in the U.S. or the Free State.

Trump maintains there is ample testing capacity in the United States if governors only could activate unused resources within their own states. Several governors and members of Congress, including Hogan, call this a fantasy and have faulted Trump or taken matters into their own hands or both.

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The federal veto

Attorney General Bill Barr opened up a new front in the federalism wars on Tuesday with comments on a radio show that suggested he'd support lawsuits against states that preserve restrictions for too long.

Trump has both sought to empower governors to manage their own states' policies and sided with small groups of protesters calling for some states to lift their stay-at-home and business restrictions.

The president said on Tuesday that he was trying to empathize with Americans fed up with staying at home or in economic peril associated with the pandemic.

All the same, Barr's comments on Tuesday revived the idea that federal officials might try to preserve a veto over states deemed too stringent or too slow in opening back up.

Trump also repeated on Tuesday that he wanted governors to act as they see fit but vowed that if he saw anything of which he disapproved, he would try to stop it.

No confirmation on Kim's health

Trump said he couldn't confirm the public reports that North Korean strongman Kim Jong Un might be in serious medical condition after what has been described as some kind of emergency heart procedure.

Trump said this in response to a question that he might try to contact the dictator, with whom the U.S. president has said he has a good relationship.

The two men negotiated but were never able to conclude an agreement under which North Korea might abandon or constrain its nuclear program.

Even so, Trump said on Tuesday that he hopes Kim is in good health.

"I'd like to see him be well. We'll see how he does."

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