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As he confronts a set of concurrent challenges, President Joe Biden receives high marks on his top priorities -- the coronavirus pandemic and the economic recovery. Still, there are warning signs for other areas of his agenda where external events have imposed new urgency, a new ABC News/Ipsos poll finds.

The president's approval lands at 72% for his handling of the coronavirus pandemic, numerically higher than the 68% of Americans who said the same earlier this month just before Congress passed his $1.9 trillion relief package, his first major legislative achievement. Only 28% disapprove of his response in the poll, which was conducted by Ipsos in partnership with ABC News using Ipsos' KnowledgePanel.

MORE: President Biden's approval on COVID-19 steady as country wary about reopening: POLL

A significant slice of the country also backs how Biden is handling distribution of the COVID-19 vaccines, with 3 in 4 Americans approving. More than one-third of the adult population (35%) has received at least one dose, according to the most recent report from the Centers for Disease Control and Prevention. On Thursday, Biden opened his first formal press conference as president by pledging to double his initial goal on administering vaccines to 200 million doses by the end of his first 100 days in office.

A clear majority of Americans (60%) also approve of Biden's stewardship on repairing the beleaguered economy, which continues to be hobbled by the coronavirus, and nearly 4 in 10 Americans disapprove.

Biden's standing on the pandemic is buttressed by overwhelming support from those who identify with his party, with about 9 in 10 Democrats approving of his handling of the public health crisis (96%), vaccine delivery (92%) and the economic response (89%). Strong majorities of independents also approve of Biden on all three fronts: 74%, 77% and 63%, respectively.

Notably, in these polarized times, a majority of Republicans (53%) also approve of Biden's handling of vaccine distribution. Fewer than half, however, view his overall response to the pandemic (44%) and his leadership on the economy (23%) positively.

Biden, at the same time, is facing some early tests in his first two months in office, finding himself underwater for his handling of gun violence after two mass shootings in a week and the surge of migrants crossing the U.S.-Mexico border, which has brought at least 18,000 unaccompanied children into U.S. custody.

An equal 57% of Americans disapprove of his approach on both issues, while just over 4 in 10 Americans approve.

MORE: Biden holds 1st formal news conference, faces questions on agenda, migrant surge

As Biden attempts to balance the various intervening forces, he signaled earlier this week that he viewed the two issues of gun control and immigration as secondary to the pandemic and its fallout, calling them "long-term problems" despite their increasing urgency.

"They've been around a long time. And what we're going to be able to do, God willing, is now begin one at a time to focus on those as well," he said at the first press conference on Thursday.

"Successful presidents -- better than me -- have been successful, in large part, because they know how to time what they're doing -- order it, decide and prioritize what needs to be done," he later added.

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Republicans are seizing on the flow of migrants at the southern border as a "crisis" -- a term that White House aides have refused to invoke while also acknowledging the troubling circumstances -- and accusing the current administration's hasty rollback of tough immigration policies implemented by former President Donald Trump as the cause.

A majority of Americans (54%) call the situation at the U.S.-Mexico border a crisis, and another 42% believe it is a serious problem but not a crisis. Only 4% of Americans say it is not a serious problem.

MORE: New photos show migrants in overcrowded Border Patrol facility in Texas

The issue of immigration is one of the most polarizing among those included in the poll, with clear majorities of Republicans (89%) and independents (54%) disapproving of Biden, while one-third of Democrats say the same.

Similarly, Biden's handling of gun violence draws disapproval from 86% of Republicans, 56% of independents and 37% of Democrats -- the highest dissatisfaction among members of his own party of the issues asked about in the survey. The disapproval from both sides is likely seen by Republicans as pursuing too many gun restrictions and by some Democrats as not acting quickly enough.

The president suggested on Thursday that he wouldn't expend his political capital on gun control reform right now, a view that appears at odds with most of the country. Roughly two-thirds of Americans in the poll said that enacting new laws to try to reduce gun violence should be a higher priority now, while 34% believe protecting gun rights should take precedence.

Biden has repeatedly underlined a desire to unify the country after four years with a divisive Trump at the helm, but so far, he's made little headway.

MORE: 3 graphics tell the story of mass shootings during the pandemic

While 30% of Americans think Biden is making the country more united, the same percentage think he is making it more divided. A plurality of 40% view his presidency as neutral on national unity.

Nearly two-thirds of Republicans (66%) think Biden is further dividing the country, and a combined 33% say he's either improving unity (5%) or having no effect (28%). Among Democrats, 95% say Biden is making the country more united (55%) or having no effect either way (40%), while 5% say he's perpetuating divisions. Independents are more split: 28% say more united, 26% say more divided and 46% say neither.

This ABC News/Ipsos poll was conducted by Ipsos Public Affairs' KnowledgePanel® March 26 to 27, 2021, in English and Spanish, among a random national sample of 517 adults. Results have a margin of sampling error of 4.9 points, including the design effect. Partisan divisions are 31-26-36%, Democrats-Republicans-independents. See the poll's topline results and details on the methodology here.

ABC News' Dan Merkle and Ken Goldstein contributed to this report.