Rajoy drew criticism from opponents and labour unions last week when he claimed that the six-year crisis was "history" now the economy was growing again.
Spain technically exited recession in mid-2013, but the unemployment rate remains extremely high at close to 24 percent.
"In many ways the crisis is history, but its consequences are not," Rajoy said on Monday after signing an accord with unions to extend long-term unemployment benefits.
"We have to be aware that the recovery has not come to everyone, nor to everyone equally," he added.
"The economic recovery will not be complete until it comes to every household and to every person who is without a job, and until it is felt in the pocket of every single Spaniard."
Rajoy's conservative government forecasts that Spain's economy, the eurozone's fourth-biggest, will grow 1.3 percent overall this year after a 1.2-percent contraction in 2013.
Rajoy said he hoped growth would top two percent next year.
That would make Spain an economic driver in Europe where other major economies such as Germany and France are struggling to strengthen their recovery.
Under the deal signed on Monday, the government agreed to pay €426 euros a month for half a year to individuals with families to support those still jobless six months after exhausting other regular unemployment benefits.
It estimated the measure could apply to some 450,000 people from January.