Stock markets rose Tuesday on both sides of the Atlantic, propelled by encouraging corporate profits, a well-received sale of government debt in Spain, a recovery in Apple stock — and, basically, the lack of any strikingly bad news.


The Dow Jones industrial average gained more than 200 points in afternoon trading to cross above the 13,000-mark for the first time since April 5. It closed with a gain of 194.13, a rise of 1.5 percent, to 13,115.54.


The broader market, as measured by the Standard & Poor’s 500-stock index, reflected a 1.6 percent advance, while the Nasdaq index shot up 1.8 percent, elevated by a 5 percent gain in Apple stock.


Analysts mostly cited the day’s reports of first-quarter earnings as the buying impetus. Coca-Cola, Johnson & Johnson and Goldman Sachs — all giants in their fields — were among those posting profits that beat expectations.


Of the 39 companies in the S.&P. 500 that reported through Tuesday morning, 74.4 percent topped analysts' forecasts, according to Thomson Reuters data. This week, 86 S.&P. 500 companies are scheduled to report.


“Earnings are coming in well enough to support the market and stabilize any significant downdraft,” Peter Kenny, managing director at Knight Capital in Jersey City, told Reuters.


But the bullish wave began in Europe earlier Tuesday, with many markets there notching gains of close to 3 percent.


Investors there were encouraged by a bond auction of short-term government debt in Madrid, which sold well although at rates that were higher than the previous auction.


The debt sale raised confidence as yields on Spain’s 10-year bond dipped below 6 percent. The interest rates rise and fall on concerns about Spain’s fiscal stability in the latest flare-up of the euro zone debt crisis.


European stocks gained after the Spanish auction. The CAC 40 in France jumped 2.7 percent, the DAX in Germany also gained 2.7 percent and the FTSE 100 in Britain rose 1.8 percent. The Euro Stoxx 50, a measure of euro zone blue chips, gained 2.9 percent.


Economic data released on Tuesday painted a mixed picture. Groundbreaking on American homes fell unexpectedly in March, the Commerce Department said, but permits for future construction rose to their highest level in three and a half years.


And a Federal Reserve report showed American industrial output was flat for a second consecutive month in March, held back by a drop in manufacturing. A measure of how fully companies are using their plants —capacity utilization — fell to 78.6 percent from 78.7 percent in February.


The strong gain on Wall Street on Tuesday nipped a two-day losing streak in the bud. The S.&P. 500 was down 1.25 percent on Friday and lost about a point on Monday.


For the Nasdaq, the Tuesday rally was erasing a 0.8 percent fall on Monday, a decline also led by Apple, which closed with a $25.10 loss, to $580.13.


But all three of the main stock market indexes are sharply higher for 2012 so far: the Dow by 7.4 percent, the S.&P. 500 by 10.6 percent and the Nasdaq by 16.8 percent.