Trump accused Democrats of loading up their rescue bill with priorities unrelated to the coronavirus.
Extra aid for the unemployed will now be $US400 ($558) a week, a cut from the $US600 ($838) that just expired.
This comes after the White House officials and congressional Democrats ended almost two weeks of talks over the fiscal aid on Friday, with the two sides still about $2 trillion apart.
The department said it would say more on its response to Trump's executive order "in the coming days".
"We support any and all relief that will come to Oregonians during this very hard time", the Oregon Employment Department said in a statement Saturday. The minority leader claimed the move will leave employees with "a huge bill" when it expires or, if the money is forgiven - as Trump said he may do in a potential second term - result in government benefit programs lacking necessary funding.
OR warned last month that if Congress allowed the expanded $600 benefits to lapse that it would take several weeks to restore the payments, even if lawmakers ultimately agree to pay them and make them retroactive. Republicans had proposed a $1 trillion plan.
But when asked about the President's executive order asking states to pay 25 per cent of the $400 unemployment relief, an official from a northeastern state run by a Democratic governor laughed. When Congress decided on the $600 payments, it was in part because many state's systems wouldn't be able to process income-based benefits in a realistic time period.
"That's generous but we want to take care of our people". "But what they're putting forth does not meet that standard", she said following stalled negotiations.
"This is not a flawless answer - we'll be the first ones to say that", Meadows said Friday as talks broke down.
The measures also included a suspension of the collection of payroll taxes - which pay for Social Security and other federal programmes - through to the end of this year, a suspension of federal student loan payments, and efforts to minimise evictions but not a moratorium. "This is the money they need".
In essence, the deferral is an interest-free loan that would have to be repaid. "Since Democrats have sabotaged backroom talks with absurd demands that would not help working people, I support President Trump exploring his options to get unemployment benefits and other relief to the people who need them the most", McConnell said in a statement.
It's far from certain that employers would actually stop withholding and submitting the payroll taxes.
Mr Trump also said Saturday his administration was looking at additional income tax and capital gains tax cuts for American taxpayers, besides the payroll tax holiday being instituted by executive order. "These workers would be hit with much bigger payments down the road".
Often an impasse in Washington is of little outcome for the public - but not so this time.
Often an impasse in Washington is of little effect for the public - but this would mean more hardship for millions of people who are losing enhanced jobless benefits and cause further damage to the economy.
White House negotiators Treasury Secretary Steven Mnuchin and Chief of Staff Mark Meadows rejected the offer.
Despite the criticism from both sites, Trump told reporters that he hopes the White House "can do something" with top Democrats "on a later date" to address the CCP (Chinese Communist Party) virus-related economic crisis. "Don't say it's your way or no way".
The breakdown in negotiations over the last several days was particularly distressing for schools trying to reopen. "And many states, because they have to chip in $100, and they don't have money, won't do it". Pelosi and Schumer stopped short of saying that Democrats would attempt to stop them in court.
According to Republican leaders, Democrats are not being honest about what caused the failure to pass additional COVID-19 relief. Four prior coronavirus response bills totaling nearly $3 trillion have won approval on bipartisan votes despite intense wrangling, but conservatives have recoiled at the prospect of another Pelosi-brokered agreement with a whopping deficit-financed cost.