Gross domestic product rose by 0.1 percent from January to March, the bank said. However, the economy remained 1.3 percent smaller than a year earlier.
The bank's assessment is provisional, based on estimates made on «available relevant data» which are due to be confirmed by the Finance Ministry next week.
On Tuesday, the Labor Ministry said unemployment fell by 24,188 in April, the first drop in eight months. A total of 4.14 million people were now claiming unemployment benefits, down from 4.17 million at the end of March.
The official unemployment rate, however, was above 20 percent for the first quarter, double the European Union average, according to the National Statistics Institute.
The bank said Spain's large budget deficit remains a concern to the European Union amid fears that the crisis over Greece's large debt load could spread to other countries with large budget shortfalls. Spain's economy is four times the size of Greece's, and last week Standard and Poor's cut Spain's credit rating from AA+ to AA.
The Bank of Spain also said the Spanish economy - which was hard hit by a collapse of the housing market - surpassed its "most acute contraction" in the first quarter of 2009.
On Wednesday the EU predicted Spain's economy would come out of recession this year.
"Its outlook features positive quarterly growth in the second quarter of 2010, partially reflecting an anticipation of consumption plans driven by the scheduled VAT rate increase on the 1st of July," the European Commission economic forecast report said.
It said that though quarterly GDP might record a technical fall in the third quarter, it would recover in the last quarter of the year.
For 2010 as a whole, real GDP is forecast to contract by one-quarter of a percent, followed by moderate positive growth of three quarters of a percent in 2011.
Spain has been the slowest of the major EU economies to emerge from recession.
Spain's overall debt stood at 53 percent of economic output last year, and its deficit was equivalent to 11.2 percent of GDP. The government has enacted a euro50 billion ($66.22 billion) austerity program aimed at getting the deficit down to the EU limit of 3 percent by 2013.
