Analysts said Wednesday's figures, which cover both services and manufacturing companies, showed that the modest recovery in the eurozone was showing increasing strength.
"Growth is increasingly reaching proper recovery speed, thanks largely to rebounding domestic demand," economist Christian Schulz at Berenberg Bank said. For the ECB, he said, the readings "decrease the need for more stimulus."
Schulz said the strong rise for the services part of the survey, to 53.1 from 52.2 in March, gave a better reading for demand from businesses and consumers at home. That's as opposed to exporters whose business depends more on the global economy.
Alarmingly low inflation of only 0.5 percent and high unemployment have raised fears the rebound was too weak to sustain itself and would require more stimulus from the European Central Bank. The eurozone grew by a quarterly rate of 0.2 percent in the fourth quarter of last year. The ECB expects the economy will grow by only 1.0 percent this year.
Still, unemployment remains painfully high at 11.9 percent for the eurozone as a whole.
The ECB, in charge of monetary policy for the euro member countries, faces pressure to cut interest rates or take other measures to increase inflation toward its goal of just under 2 percent.
Low inflation is a sign of continuing weak demand, and can make it harder for indebted countries, companies and consumers to pay down debt. Some economists fear that if further measures are not taken, the eurozone could slip into outright deflation, a crippling downward price spiral that kills off growth and jobs. Despite the recent falls in inflation, the ECB says deflation is unlikely.
Despite the broadly positive survey, Markit's chief economist Chris Williamson warned that companies were still cutting prices.
"There will be growing fears that deflationary pressures are intensifying," he said. One problem is a recently stronger euro that lowers the prices of imported goods. The euro has been trading near two and a half year highs against the dollar in recent weeks. Currently, one euro is worth $1.3825.
Some analysts still say the ECB may yet cut its benchmark interest rate from its current record low of 0.25 percent or take other action in the coming months. That could both stimulate growth and push the euro exchange rate down.
The ECB's rate-setting council next meets May 8.