By Andrew Restuccia

WASHINGTON -- The Trump administration is examining proposals to provide cash incentives to encourage unemployed Americans to return to work, according to a top economic adviser, as the White House looks to revive the economy.

The-back to-work bonus is "something we're looking at very carefully," Larry Kudlow, the director of the White House National Economic Council, said during an interview on Fox News.

Mr. Kudlow made the comments after he was asked about a proposal by Sen. Rob Portman (R., Ohio) to provide a temporary $450-a-week bonus for unemployed workers returning to work, on top of their wages.

Republicans joined with Democrats in March to pass an economic-aid bill that included enhanced unemployment payments of $600 a week through July. Democrats want to extend that funding into next year. The White House and top GOP lawmakers have rejected that plan but have said they are open to other ideas.

"The trouble with the $600 plus-up -- and maybe we needed it in that emergency period -- but frankly it's a major disincentive to go back to work," said Mr. Kudlow. He predicted that provision won't be included in the next coronavirus-response package. He also said President Trump remains interested in a payroll-tax cut, an idea that has gained little traction among Democratic or Republican lawmakers.

House Democrats earlier this month passed a $3 trillion aid bill that includes extending the enhanced jobless benefits as well as an additional round of direct payments to most U.S. households and $1 trillion in aid to states and cities. They argue Congress needs to approve more aid now, to tide people over into next year.

"Sen. [Mitch] McConnell ought to take it up, ought to consider it, and let the Senate work its will," said House Majority Leader Steny Hoyer (D., Md.) on Tuesday.

Senate Republicans have taken a go-slow approach on further aid as they bet on the economy reopening, and they have emphasized protecting businesses from coronavirus-related lawsuits.

"There's still a likelihood that more will be needed," said Senate Majority Leader McConnell (R., Ky.) at an appearance Tuesday in his home state, while reiterating that the House bill was a nonstarter. He called short-term liability shields "absolutely essential" for health-care providers and other businesses.

The Trump administration in April released guidelines that said states should move to the first phase of reopening after exhibiting a downward trend of documented cases of Covid-19 or positive tests over a two-week period.

All 50 states have begun taking steps to reopen, even though many of them have yet to meet the administration's recommendations for reopening. Asked whether the president is concerned about states not following the guidelines, a White House official said, "The guidelines are just that -- they are guidelines to maintain public health. They are not mandatory."

White House press secretary Kayleigh McEnany encouraged Americans to follow the administration's social-distancing guidelines following a Memorial Day weekend in which large groups gathered in some states in violation of the recommendations.

"There are ways to do this and the president would underscore to everyone that we should be taking into account these measures," she said during a Tuesday White House briefing.

The president and his advisers believe a speedy reopening will boost the U.S. economy, potentially beginning to reverse the negative trends ahead of November's election. They have predicted that the U.S. will see strong growth in the third quarter of the year.

President Trump on Tuesday defended his administration's response to the coronavirus as the U.S. death toll neared 100,000. He argued that the number of deaths would be much higher if he hadn't limited travel from China in January.

The president has come under repeated criticism from public-health officials, lawmakers and others for his response to the outbreak, with experts faulting the administration for not doing more to set up a robust testing system earlier. Experts have also said many early cases in New York came from European nations, not China.

Meanwhile, a senior White House official who tested positive for the Covid-19 returned to work on Tuesday following a self-quarantine. Katie Miller, Vice President Mike Pence's press secretary, said she tested negative for the virus three times before returning.

Ms. McEnany told reporters that she didn't know if other White House staffers had tested positive for the virus and might not be able to get that information for privacy reasons.

Write to Andrew Restuccia at Andrew.Restuccia@wsj.com