IMF managing director Christine Lagarde says failure to raise the US debt ceiling would be a far worse threat to the global economy than the current shutdown.
The shutdown is due to a budget standoff between President Barack Obama and Congress.
But a worse problem looms: the US will run out of money if there is no agreement to raise the borrowing limit.
Ms Lagarde's comments were echoed by the US Treasury.
It says a debt default could lead to a financial crisis as bad as 2008 or worse.
Mr Obama emphasised that gloomy message in a separate speech on Thursday.
"As reckless as a government shutdown is, as many people as are being hurt by a government shutdown, an economic shutdown that results from default would be dramatically worse," he said.
Mr Obama and congressional leaders have been in political deadlock for days, which has had the effect of freezing non-essential US government functions.
The US government closed non-essential operations on Tuesday after Congress failed to strike a deal on a new budget.
The shutdown has left more than 700,000 employees on unpaid leave and closed national parks, tourist sites, government websites, office buildings, and more.
For US economic watchers, a widely tracked indicator - the monthly US jobs report - has been delayed due to the shutdown, it was announced on Thursday.
However, while this budget crisis rages in Washington DC, another, more dangerous, one looms in the coming weeks.
On 17 October, the US government will run out of cash to pay its bills - unless the debt ceiling is raised.
In a speech looking ahead to a decade of challenges for the world economy, Ms Lagarde said that the US government needed to fix its finances for the long term.
She said it was "mission critical" that the US agrees a new debt ceiling.
But as she has often said before, there should not be too much change in the short term because that could undermine the economic recovery.
On the prospects for the world economy in general terms Ms Lagarde was cautiously positive.
She added that, although the global economic outlook remained subdued, there were signs that growth was looking up and financial stability returning.
She said not only was the US picking up steam, but the Eurozone was too, with a growth forecast of 1% next year. Even Japan, she said, was beginning to improve - albeit all three areas needed to make policy changes.
The IMF's latest economic forecasts will be released in a few days and will give a more detailed view of global economic health and prospects.
'End this shutdown right now'
To ensure that the shutdown impasse does not bleed into negotiations over the debt ceiling, Mr Obama used his speech to call on the speaker of the House of Representatives, John Boehner, to bring a spending bill to a vote.
"Take a vote, stop this farce, and end this shutdown right now," implored Mr Obama, speaking from the floor of a construction business that has been hurt by the shutdown.
Mr Obama added that in his view, unlike budget battles of the past, the shutdown was not about ideological differences relating to how much the federal government should be spending - noting deficits have been falling at their fastest pace in 60 years.
"This not about spending and this is not about fiscal responsibility, this whole thing is about one thing: the Republican obsession with dismantling the Affordable Care Act," he said, citing his signature domestic legislative achievement, which expands health care coverage for millions of Americans.
Impact 'more than a generation'
In its report, the US Treasury warned: "A default would be unprecedented and has the potential to be catastrophic."
"Credit markets could freeze, the value of the dollar could plummet, US interest rates could skyrocket, the negative spillovers could reverberate around the world, and there might be a financial crisis and recession that could echo the events of 2008 or worse."
The report said that if this were to happen, the impact could last for "more than a generation."
Already, the cost of US borrowing in the short term has increased.
Essentially, the US government is paying less to borrow for six months than it is paying to borrow for one month - an indication that investors are worried about the near-term prospects of a US debt default on 17 October, which would put the security of one-month Treasury bonds in doubt.
Some bank analysts have termed the next month the "debt ceiling danger zone".
Traditionally, investors view this as an "inverted yield curve" which is typically viewed as a harbinger of a recession.
The current shutdown is costing the US economy an estimated $300m a day.
According to Goldman Sachs, it could shave as much as 0.2% from GDP each week the government is closed.