Americans have been borrowing money at rates not seen since the recession began, but they are vigilant about paying their debts on time, according to data released Tuesday by the Federal Reserve Bank of New York.

The findings from a government survey suggest that after a long period of paying down debts and building up savings, U.S. households have resumed borrowing with a keen awareness of past debt burdens.

Debt tied to credit cards, mortgages, student loans and auto loans climbed $241 billion, or 2.1 percent, to $11.52 trillion in the last three months of 2013, marking the biggest gain since the third quarter of 2007, according to the survey.

Much of the growth during the quarter was attributed to a $152 billion surge in mortgage balances, the largest component of household debt. The increase was mostly fueled by a decline in foreclosures and bankruptcies, according to the New York Fed.

Government economists said foreclosures are now at the lowest levels since the end of 2005. Americans have been catching up on their monthly mortgage payments, with delinquency rates tumbling from 4.3 percent in the third quarter to 3.4 percent in the last three months of the year.

“Foreclosures and bankruptcies declining indicate that people are now in a better position to make a major purchase, and the lenders apparently agree,” said Gail Cunningham of the National Foundation for Credit Counseling. “The question that haunts me is, why are they in a better position? Did they learn the hard lesson . . . or are [they] simply going to pick up where they left off?”

There is evidence that consumers are exhibiting more caution. Economists at the New York Fed compared borrowing behavior in 2006 with that in 2013 and discovered some stark differences. Whereas all types of consumers took on large amounts of housing debt before the crisis, these days, most of the growth is among those with high credit scores.

Consumers with high scores drove the modest increase in mortgage balances last year, while many of those with low scores saw their debt loads fall as the result of foreclosure. A similar trend emerged for credit card balances, which climbed $4 billion, to $683 billion, in 2013 because of borrowers with high credit scores.

Another indicator of cautious optimism among consumers is the decline of new mortgage and auto loan originations, which fell in the fourth quarter to $452 billion and $88 billion respectively. Economists suspect that higher interest rates kept Americans on the sidelines.

Still, the number of credit inquiries for car loans, an indicator of consumer credit demand, remained virtually unchanged from the third quarter at 169 million, according to the survey.

Auto debt grew $18 billion, to $863 billion, in the last three months of the year, continuing the strong growth since mid-2011. The increase in lending corresponds with the robust auto sales of 2013, driven by a surge in leasing and pent-up demand for vehicles.

Of the major types of household debt, the rate of delinquent payments is highest among student loans, at 11.5 percent, despite a 0.3 percent decline from the third quarter. The stubbornly high rate of late payments suggests that the lackluster job market and high education costs are weighing heavily on people who took out loans to pay for school.

“You have a lot of people that are getting out of college and having a real hard time in the labor market. They’re sitting there with $40,000 or $50,000 in debt that they can’t easily discharge,” said Dean Baker, co-founder of the Center for Economic and Policy Research. “That’s going to be a big burden.”

Education borrowing soared $114 billion, to $1.08 trillion, from the fourth quarter of 2012 to the end of last year. Student debt grew $53 billion in the last three months of the year, according to the New York Fed.

Overall, consumer debt is 9.1 percent below its peak of $12.68 trillion in the third quarter of 2008.

“At some point, it was inevitable that consumers were going to begin borrowing again. The data suggests that tipping point may have occurred,” Cunningham said. “Consumers need to exercise caution, however, as a lower balance does not necessarily indicate that the time to put their toes back into the financial water is at hand.”